🔗 Problem

Problem: Solve the following equation for the variable u: 122 = 92 + 28 * u

Gemma 2B:

    To solve the equation \( 122 = 92 + 28u \) for the variable \( u \), follow these steps:

    1. Subtract 92 from both sides of the equation to isolate the term with \( u \):
       \[
       122 - 92 = 28u
       \]

    2. Simplify the left side:
       \[
       30 = 28u
       \]

    3. Divide both sides by 28 to solve for \( u \):
       \[
       u = \frac{30}{28}
       \]

    4. Simplify the fraction:
       \[
       u = \frac{15}{14}
       \]

    ### Answer: \( \frac{15}{14} \)

Expected answer: 15/14

Correct? Yes

🔗 Problem

Problem: Solve the following equation for i: 42 = ((35 * i) - 34)

Gemma 2B:

    To solve the equation \( 42 = 35i - 34 \) for \( i \), follow these steps:

    1. Start with the given equation:
       \[
       42 = 35i - 34
       \]

    2. Add 34 to both sides of the equation to isolate the term with \( i \):
       \[
       42 + 34 = 35i
       \]

    3. Simplify the left side:
       \[
       76 = 35i
       \]

    4. Divide both sides by 35 to solve for \( i \):
       \[
       i = \frac{76}{35}
       \]

    5. Simplify the fraction if possible:
       \[
       i = \frac{76}{35}
       \]

    ### Answer: \( \frac{76}{35} \)

Expected answer: 76/35

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of r: 94 = 41 + 6 * r

Gemma 2B:

    To solve the equation \( 94 = 41 + 6r \) for \( r \), follow these steps:

    1. Subtract 41 from both sides of the equation to isolate the term with \( r \):
       \[
       94 - 41 = 6r
       \]

    2. Simplify the left side:
       \[
       53 = 6r
       \]

    3. Divide both sides by 6 to solve for \( r \):
       \[
       r = \frac{53}{6}
       \]

    4. Simplify the fraction if possible:
       \[
       r = 8.8333\ldots \quad \text{(or as a fraction, } \frac{53}{6} \text{)}
       \]

    ### Answer: \( r = \frac{53}{6} \) or \( r \approx 8.8333 \)

Expected answer: 53/6

Correct? Yes

🔗 Problem

Problem: Determine the value of "i" from the following equation: 158 = ((19 * i) + 94)

Gemma 2B:

    To determine the value of \( i \) from the equation \( 158 = 19i + 94 \), we need to isolate \( i \). Here are the steps:

    1. Start with the given equation:
       \[
       158 = 19i + 94
       \]

    2. Subtract 94 from both sides to isolate the term with \( i \):
       \[
       158 - 94 = 19i
       \]

    3. Simplify the left side:
       \[
       64 = 19i
       \]

    4. Divide both sides by 19 to solve for \( i \):
       \[
       i = \frac{64}{19}
       \]

    5. Simplify the fraction if possible. In this case, \( \frac{64}{19} \) is already in its simplest form.

    ### Answer: \(\frac{64}{19}\)

Expected answer: 64/19

Correct? Yes

🔗 Problem

Problem: Solve the following equation for 'q': 134 = ((30 * q) + 54)

Gemma 2B:

    To solve the equation \( 134 = 30q + 54 \) for \( q \), follow these steps:

    1. Subtract 54 from both sides of the equation to isolate the term with \( q \):
       \[
       134 - 54 = 30q
       \]

    2. Simplify the left side:
       \[
       80 = 30q
       \]

    3. Divide both sides by 30 to solve for \( q \):
       \[
       q = \frac{80}{30}
       \]

    4. Simplify the fraction:
       \[
       q = \frac{8}{3}
       \]

    ### Answer: \( \frac{8}{3} \)

Expected answer: 8/3

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation to find the value of y: 94 = (27 + y)

Gemma 2B:

    To solve the linear equation \( 94 = 27 + y \), we need to isolate \( y \).

    Step 1: Subtract 27 from both sides of the equation to isolate \( y \):
    \[ 94 - 27 = y \]

    Step 2: Perform the subtraction:
    \[ 67 = y \]

    Thus, the value of \( y \) is 67.

    ### Answer: 67

Expected answer: 67

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of h: 9 = ((23 * h) - 70)

Gemma 2B:

    To solve the linear equation \( 9 = 23h - 70 \) for \( h \), follow these steps:

    1. Start with the given equation:
       \[
       9 = 23h - 70
       \]

    2. Add 70 to both sides of the equation to isolate the term with \( h \):
       \[
       9 + 70 = 23h - 70 + 70
       \]
       Simplifying the left side:
       \[
       79 = 23h
       \]

    3. Divide both sides by 23 to solve for \( h \):
       \[
       \frac{79}{23} = \frac{23h}{23}
       \]
       Simplifying the right side:
       \[
       h = \frac{79}{23}
       \]

    4. Perform the division:
       \[
       h = \frac{79}{23} \approx 3.4348
       \]

    ### Answer: \( h \approx 3.4348 \)

Expected answer: 79/23

Correct? No

🔗 Problem

Problem: Solve the following equation to find the value of t: 92 = 33 * t + 26

Gemma 2B:

    To solve the equation \( 92 = 33t + 26 \) for \( t \), follow these steps:

    1. Subtract 26 from both sides of the equation to isolate the term with \( t \):
       \[
       92 - 26 = 33t
       \]
       Simplifying the left side:
       \[
       66 = 33t
       \]

    2. Divide both sides by 33 to solve for \( t \):
       \[
       t = \frac{66}{33}
       \]
       Simplifying the fraction:
       \[
       t = 2
       \]

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation to find the value of e: 123 = ((15 * e) + 29).

Gemma 2B:

    To solve the linear equation \( 123 = 15e + 29 \), we need to isolate the variable \( e \). Here are the steps:

    1. Subtract 29 from both sides of the equation to get rid of the constant term on the right side:
       \[
       123 - 29 = 15e
       \]

    2. Simplify the left side:
       \[
       94 = 15e
       \]

    3. Divide both sides by 15 to solve for \( e \):
       \[
       e = \frac{94}{15}
       \]

    4. Simplify the fraction if possible:
       \[
       e = \frac{94}{15} \approx 6.27
       \]

    ### Answer: \( e = \frac{94}{15} \) or approximately 6.27.

Expected answer: 94/15

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of 'k': 16 = ((75 * k) - 80)

Gemma 2B:

    To solve the equation \( 16 = 75k - 80 \) for \( k \), follow these steps:

    1. Add 80 to both sides of the equation to isolate the term with \( k \):
       \[
       16 + 80 = 75k - 80 + 80
       \]
       Simplifying this, we get:
       \[
       96 = 75k
       \]

    2. Divide both sides of the equation by 75 to solve for \( k \):
       \[
       k = \frac{96}{75}
       \]

    3. Simplify the fraction:
       \[
       k = \frac{96 \div 3}{75 \div 3} = \frac{32}{25}
       \]

    ### Answer: \( \frac{32}{25} \)

Expected answer: 32/25

Correct? Yes

🔗 Problem

Problem: Solve for q in the following equation: 131 = ((5 * q) + 89)

Gemma 2B:

    To solve for \( q \) in the equation \( 131 = 5q + 89 \), follow these steps:

    1. Subtract 89 from both sides of the equation to isolate the term with \( q \):
       \[
       131 - 89 = 5q
       \]

    2. Simplify the left side:
       \[
       42 = 5q
       \]

    3. Divide both sides by 5 to solve for \( q \):
       \[
       q = \frac{42}{5}
       \]

    4. Simplify the fraction:
       \[
       q = 8.4
       \]

    ### Answer: 8.4

Expected answer: 42/5

Correct? Yes

🔗 Problem

Problem: Find the value of p that satisfies the following equation: 147 = ((38 * p) + 56)

Gemma 2B:

    To find the value of \( p \) that satisfies the equation \( 147 = (38p + 56) \), we need to isolate \( p \). Here are the steps:

    1. Start with the given equation:
       \[
       147 = 38p + 56
       \]

    2. Subtract 56 from both sides to isolate the term with \( p \):
       \[
       147 - 56 = 38p
       \]

    3. Simplify the left side:
       \[
       91 = 38p
       \]

    4. Divide both sides by 38 to solve for \( p \):
       \[
       p = \frac{91}{38}
       \]

    5. Simplify the fraction if possible:
       \[
       p = \frac{91}{38} = 2.394736842105263
       \]

    ### Answer: 2.394736842105263

Expected answer: 91/38

Correct? No

🔗 Problem

Problem: Solve the following equation to find the value of 'j': 76 = 42 * j + 23

Gemma 2B:

    To solve the equation \( 76 = 42j + 23 \) for \( j \), follow these steps:

    1. Subtract 23 from both sides of the equation to isolate the term with \( j \):
       \[
       76 - 23 = 42j
       \]
       Simplifying the left side:
       \[
       53 = 42j
       \]

    2. Divide both sides by 42 to solve for \( j \):
       \[
       j = \frac{53}{42}
       \]

    3. Simplify the fraction if possible. In this case, 53 and 42 have no common factors other than 1, so the fraction is already in its simplest form:
       \[
       j = \frac{53}{42}
       \]

    ### Answer: \(\frac{53}{42}\)

Expected answer: 53/42

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of 'l': 138 = 43 + 25 * l

Gemma 2B:

    To solve the equation \( 138 = 43 + 25l \) for \( l \), follow these steps:

    1. Subtract 43 from both sides of the equation to isolate the term with \( l \):
       \[
       138 - 43 = 25l
       \]

    2. Simplify the left side:
       \[
       95 = 25l
       \]

    3. Divide both sides by 25 to solve for \( l \):
       \[
       l = \frac{95}{25}
       \]

    4. Simplify the fraction:
       \[
       l = 3.8
       \]

    ### Answer: 3.8

Expected answer: 19/5

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the unknown w: 80 = ((24 * w) + 35)

Gemma 2B:

    To solve the equation \( 80 = 24w + 35 \) for \( w \), follow these steps:

    1. Subtract 35 from both sides of the equation to isolate the term with \( w \):
       \[
       80 - 35 = 24w
       \]
       Simplifying the left side:
       \[
       45 = 24w
       \]

    2. Divide both sides by 24 to solve for \( w \):
       \[
       w = \frac{45}{24}
       \]

    3. Simplify the fraction:
       \[
       w = \frac{15}{8}
       \]

    ### Answer: \(\frac{15}{8}\)

Expected answer: 15/8

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation to find the value of x: 77 = (33 + (14 * x))

Gemma 2B:

    To solve the linear equation \( 77 = 33 + 14x \), we need to isolate \( x \). Here are the steps:

    1. Subtract 33 from both sides of the equation to get rid of the constant term on the right side:
       \[
       77 - 33 = 33 + 14x - 33
       \]
       Simplifying this, we get:
       \[
       44 = 14x
       \]

    2. Next, divide both sides of the equation by 14 to solve for \( x \):
       \[
       \frac{44}{14} = \frac{14x}{14}
       \]
       Simplifying this, we get:
       \[
       x = \frac{44}{14}
       \]

    3. Simplify the fraction:
       \[
       x = \frac{22}{7}
       \]

    ### Answer: \(\frac{22}{7}\)

Expected answer: 22/7

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation to find the value of y: 110 = 12 + 88 * y

Gemma 2B:

    To solve the linear equation \( 110 = 12 + 88y \), we need to isolate the variable \( y \). Here are the steps:

    1. Subtract 12 from both sides of the equation to get rid of the constant term on the right side:
       \[
       110 - 12 = 88y
       \]
       Simplifying the left side:
       \[
       98 = 88y
       \]

    2. Divide both sides of the equation by 88 to solve for \( y \):
       \[
       y = \frac{98}{88}
       \]

    3. Simplify the fraction:
       \[
       y = \frac{49}{44}
       \]

    So, the value of \( y \) is \( \frac{49}{44} \).

    ### Answer: \(\frac{49}{44}\)

Expected answer: 49/44

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable 's': 179 = 82 * s + 80

Gemma 2B:

    To solve the linear equation \( 179 = 82s + 80 \) for the variable \( s \), follow these steps:

    1. Subtract 80 from both sides of the equation to isolate the term with \( s \):
       \[
       179 - 80 = 82s + 80 - 80
       \]
       Simplifying this, we get:
       \[
       99 = 82s
       \]

    2. Divide both sides of the equation by 82 to solve for \( s \):
       \[
       s = \frac{99}{82}
       \]

    3. Simplify the fraction if possible. In this case, 99 and 82 have no common factors other than 1, so the fraction is already in its simplest form:
       \[
       s = \frac{99}{82}
       \]

    ### Answer: \(\frac{99}{82}\)

Expected answer: 99/82

Correct? Yes

🔗 Problem

Problem: Solve the following equation for m: 129 = 26 * m + 66

Gemma 2B:

    To solve the equation \( 129 = 26m + 66 \) for \( m \), follow these steps:

    1. Subtract 66 from both sides of the equation to isolate the term with \( m \):
       \[
       129 - 66 = 26m
       \]
       Simplifying the left side:
       \[
       63 = 26m
       \]

    2. Divide both sides of the equation by 26 to solve for \( m \):
       \[
       m = \frac{63}{26}
       \]

    3. Simplify the fraction if possible. In this case, 63 and 26 have no common factors other than 1, so the fraction is already in its simplest form:
       \[
       m = \frac{63}{26}
       \]

    ### Answer: \( \frac{63}{26} \)

Expected answer: 63/26

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for q: 82 = ((27 * q) - 17)

Gemma 2B:

    To solve the linear equation for \( q \):

    \[ 82 = 27q - 17 \]

    First, isolate the term with \( q \) by adding 17 to both sides of the equation:

    \[ 82 + 17 = 27q - 17 + 17 \]

    This simplifies to:

    \[ 99 = 27q \]

    Next, solve for \( q \) by dividing both sides by 27:

    \[ q = \frac{99}{27} \]

    Simplify the fraction:

    \[ q = \frac{99 \div 9}{27 \div 9} = \frac{11}{3} \]

    ### Answer: \(\frac{11}{3}\)

Expected answer: 11/3

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable k: 141 = (64 + (22 * k))

Gemma 2B:

    To solve the linear equation for the variable \( k \):

    \[ 141 = 64 + 22k \]

    First, isolate the term containing \( k \) by subtracting 64 from both sides of the equation:

    \[ 141 - 64 = 22k \]

    Simplify the left side:

    \[ 77 = 22k \]

    Next, solve for \( k \) by dividing both sides by 22:

    \[ k = \frac{77}{22} \]

    Simplify the fraction:

    \[ k = 3.5 \]

    ### Answer: 3.5

Expected answer: 7/2

Correct? Yes

🔗 Problem

Problem: Determine the value of 'v' by solving this linear equation: 175 = 91 + 45 * v

Gemma 2B:

    To solve for \( v \) in the equation \( 175 = 91 + 45v \), follow these steps:

    1. Subtract 91 from both sides of the equation to isolate the term with \( v \):
       \[
       175 - 91 = 45v
       \]

    2. Simplify the left side:
       \[
       84 = 45v
       \]

    3. Divide both sides by 45 to solve for \( v \):
       \[
       v = \frac{84}{45}
       \]

    4. Simplify the fraction by finding the greatest common divisor (GCD) of 84 and 45, which is 3:
       \[
       v = \frac{84 \div 3}{45 \div 3} = \frac{28}{15}
       \]

    ### Answer: \(\frac{28}{15}\)

Expected answer: 28/15

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the value of k: 50 = ((63 * k) - 18)

Gemma 2B:

    To solve the equation \( 50 = 63k - 18 \) for \( k \), follow these steps:

    1. Start by isolating the term with \( k \) on one side of the equation. Add 18 to both sides of the equation:
       \[
       50 + 18 = 63k - 18 + 18
       \]
       Simplifying this, we get:
       \[
       68 = 63k
       \]

    2. Next, solve for \( k \) by dividing both sides of the equation by 63:
       \[
       k = \frac{68}{63}
       \]

    Thus, the value of \( k \) is:
    ### Answer: \(\frac{68}{63}\)

Expected answer: 68/63

Correct? Yes

🔗 Problem

Problem: Solve the following equation for l: 65 = ((8 * l) - 10)

Gemma 2B:

    To solve the equation \( 65 = 8l - 10 \) for \( l \), follow these steps:

    1. Start with the given equation:
       \[
       65 = 8l - 10
       \]

    2. Add 10 to both sides of the equation to isolate the term with \( l \):
       \[
       65 + 10 = 8l - 10 + 10
       \]
       Simplifying this, we get:
       \[
       75 = 8l
       \]

    3. Divide both sides of the equation by 8 to solve for \( l \):
       \[
       \frac{75}{8} = \frac{8l}{8}
       \]
       Simplifying this, we get:
       \[
       l = \frac{75}{8}
       \]

    4. Simplify the fraction if possible:
       \[
       l = 9.375
       \]

    ### Answer: 9.375

Expected answer: 75/8

Correct? Yes

🔗 Problem

Problem: Solve the following equation: 5 = ((10 * u) - 34)

Gemma 2B:

    To solve the equation \( 5 = 10u - 34 \), we need to isolate the variable \( u \). Here are the steps:

    1. Start with the given equation:
       \[
       5 = 10u - 34
       \]

    2. Add 34 to both sides of the equation to move the constant term on the right side to the left side:
       \[
       5 + 34 = 10u - 34 + 34
       \]
       Simplifying this, we get:
       \[
       39 = 10u
       \]

    3. Divide both sides of the equation by 10 to solve for \( u \):
       \[
       \frac{39}{10} = \frac{10u}{10}
       \]
       Simplifying this, we get:
       \[
       3.9 = u
       \]

    ### Answer: 3.9

Expected answer: 39/10

Correct? Yes

🔗 Problem

Problem: Solve the following problem in linear equations for variable 'a': 91 = 9 * a + 61

Gemma 2B:

    To solve the equation \( 91 = 9a + 61 \) for the variable \( a \), follow these steps:

    1. Subtract 61 from both sides of the equation to isolate the term with \( a \):
       \[
       91 - 61 = 9a + 61 - 61
       \]
       Simplifying this, we get:
       \[
       30 = 9a
       \]

    2. Divide both sides of the equation by 9 to solve for \( a \):
       \[
       \frac{30}{9} = \frac{9a}{9}
       \]
       Simplifying this, we get:
       \[
       a = \frac{30}{9} = \frac{10}{3}
       \]

    ### Answer: \( \frac{10}{3} \)

Expected answer: 10/3

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable i: 157 = 53 * i + 61

Gemma 2B:

    To solve the linear equation for the variable \( i \), we need to isolate \( i \) on one side of the equation. Here are the steps:

    1. Start with the given equation:
       \[
       157 = 53i + 61
       \]

    2. Subtract 61 from both sides to isolate the term with \( i \):
       \[
       157 - 61 = 53i
       \]

    3. Simplify the left side:
       \[
       96 = 53i
       \]

    4. Divide both sides by 53 to solve for \( i \):
       \[
       i = \frac{96}{53}
       \]

    5. Simplify the fraction if possible. In this case, 96 and 53 have no common factors other than 1, so the fraction is already in its simplest form.

    ### Answer: \( \frac{96}{53} \)

Expected answer: 96/53

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of q: 71 = ((24 * q) + 14)

Gemma 2B:

    To solve the linear equation \( 71 = 24q + 14 \) for \( q \), follow these steps:

    1. Subtract 14 from both sides of the equation to isolate the term with \( q \):
       \[
       71 - 14 = 24q
       \]
       Simplifying the left side:
       \[
       57 = 24q
       \]

    2. Divide both sides by 24 to solve for \( q \):
       \[
       q = \frac{57}{24}
       \]

    3. Simplify the fraction if possible:
       \[
       q = \frac{57}{24} = \frac{19}{8}
       \]

    ### Answer: \(\frac{19}{8}\)

Expected answer: 19/8

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of i: 163 = 96 + 14 * i

Gemma 2B:

    To solve the linear equation \( 163 = 96 + 14i \) for \( i \), follow these steps:

    1. Subtract 96 from both sides of the equation to isolate the term with \( i \):
       \[
       163 - 96 = 14i
       \]

    2. Simplify the left side:
       \[
       67 = 14i
       \]

    3. Divide both sides by 14 to solve for \( i \):
       \[
       i = \frac{67}{14}
       \]

    4. Simplify the fraction if possible:
       \[
       i = \frac{67}{14}
       \]

    Since 67 and 14 have no common factors other than 1, the fraction is already in its simplest form.

    ### Answer: \( \frac{67}{14} \)

Expected answer: 67/14

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of e: 59 = (70 * e) - 23

Gemma 2B:

    To solve the linear equation \( 59 = 70e - 23 \) for \( e \), follow these steps:

    1. Start by isolating the term with \( e \) on one side of the equation. Add 23 to both sides of the equation:
       \[
       59 + 23 = 70e - 23 + 23
       \]
       Simplifying this, we get:
       \[
       82 = 70e
       \]

    2. Next, solve for \( e \) by dividing both sides of the equation by 70:
       \[
       e = \frac{82}{70}
       \]

    3. Simplify the fraction:
       \[
       e = \frac{41}{35}
       \]

    Thus, the value of \( e \) is:
    ### Answer: \(\frac{41}{35}\)

Expected answer: 41/35

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for o: 147 = 36 * o + 74

Gemma 2B:

    To solve the linear equation for \( o \), we need to isolate \( o \) on one side of the equation. Here are the steps:

    1. Start with the given equation:
       \[
       147 = 36o + 74
       \]

    2. Subtract 74 from both sides to isolate the term with \( o \):
       \[
       147 - 74 = 36o
       \]

    3. Simplify the left side:
       \[
       73 = 36o
       \]

    4. Divide both sides by 36 to solve for \( o \):
       \[
       o = \frac{73}{36}
       \]

    Thus, the value of \( o \) is:
    ### Answer: \(\frac{73}{36}\)

Expected answer: 73/36

Correct? Yes

🔗 Problem

Problem: Solve the following equation: 71 = 93 - (13 * d)

Gemma 2B:

    To solve the equation \( 71 = 93 - (13 \cdot d) \), we need to isolate the variable \( d \). Here are the steps:

    1. Start with the given equation:
       \[
       71 = 93 - 13d
       \]

    2. Subtract 93 from both sides to isolate the term involving \( d \):
       \[
       71 - 93 = -13d
       \]

    3. Simplify the left side:
       \[
       -22 = -13d
       \]

    4. Divide both sides by -13 to solve for \( d \):
       \[
       d = \frac{-22}{-13}
       \]

    5. Simplify the fraction:
       \[
       d = \frac{22}{13}
       \]

    ### Answer: \(\frac{22}{13}\)

Expected answer: 22/13

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of n: 118 = 64 + 6 * n

Gemma 2B:

    To solve the equation \( 118 = 64 + 6n \), we need to isolate the variable \( n \). Here are the steps:

    1. Subtract 64 from both sides of the equation to get:
       \[
       118 - 64 = 6n
       \]

    2. Simplify the left side:
       \[
       54 = 6n
       \]

    3. Divide both sides by 6 to solve for \( n \):
       \[
       n = \frac{54}{6}
       \]

    4. Simplify the division:
       \[
       n = 9
       \]

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of 'd': 61 = ((5 * d) - 7)

Gemma 2B:

    To solve the equation \( 61 = (5d - 7) \), we need to isolate the variable \( d \). Here are the steps:

    1. Start with the given equation:
       \[
       61 = 5d - 7
       \]

    2. Add 7 to both sides of the equation to eliminate the constant term on the right side:
       \[
       61 + 7 = 5d - 7 + 7
       \]
       Simplifying this, we get:
       \[
       68 = 5d
       \]

    3. Divide both sides of the equation by 5 to solve for \( d \):
       \[
       \frac{68}{5} = \frac{5d}{5}
       \]
       Simplifying this, we get:
       \[
       d = \frac{68}{5}
       \]

    4. Simplify the fraction:
       \[
       d = 13.6
       \]

    ### Answer: 13.6

Expected answer: 68/5

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of z: 79 = ((8 * z) - 18)

Gemma 2B:

    To solve the linear equation \( 79 = 8z - 18 \) for \( z \), follow these steps:

    1. Start with the given equation:
       \[
       79 = 8z - 18
       \]

    2. Add 18 to both sides of the equation to isolate the term with \( z \):
       \[
       79 + 18 = 8z - 18 + 18
       \]
       Simplifying the left side:
       \[
       97 = 8z
       \]

    3. Divide both sides by 8 to solve for \( z \):
       \[
       \frac{97}{8} = z
       \]

    4. Simplify the fraction if possible:
       \[
       z = 12.125
       \]

    ### Answer: 12.125

Expected answer: 97/8

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of z: 129 = ((2 * z) + 63)

Gemma 2B:

    To solve the linear equation for \( z \), we start with the given equation:

    \[ 129 = 2z + 63 \]

    First, we need to isolate the term containing \( z \). We do this by subtracting 63 from both sides of the equation:

    \[ 129 - 63 = 2z \]

    Simplifying the left side:

    \[ 66 = 2z \]

    Next, we solve for \( z \) by dividing both sides by 2:

    \[ \frac{66}{2} = z \]

    Simplifying the right side:

    \[ z = 33 \]

    ### Answer: 33

Expected answer: 33

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for e: 127 = (29 + (32 * e))

Gemma 2B:

    To solve the linear equation \(127 = 29 + 32e\), we need to isolate the variable \(e\). Here are the steps:

    1. Subtract 29 from both sides of the equation to isolate the term with \(e\):
       \[
       127 - 29 = 32e
       \]

    2. Simplify the left side:
       \[
       98 = 32e
       \]

    3. Divide both sides by 32 to solve for \(e\):
       \[
       e = \frac{98}{32}
       \]

    4. Simplify the fraction:
       \[
       e = \frac{49}{16}
       \]

    ### Answer: \(\frac{49}{16}\)

Expected answer: 49/16

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of x: 30 = ((50 * x) - 35)

Gemma 2B:

    To solve the linear equation \( 30 = 50x - 35 \), follow these steps:

    1. Add 35 to both sides of the equation to isolate the term with \( x \):
       \[
       30 + 35 = 50x - 35 + 35
       \]
       Simplifying this, we get:
       \[
       65 = 50x
       \]

    2. Divide both sides by 50 to solve for \( x \):
       \[
       x = \frac{65}{50}
       \]

    3. Simplify the fraction:
       \[
       x = \frac{65 \div 5}{50 \div 5} = \frac{13}{10} = 1.3
       \]

    ### Answer: 1.3

Expected answer: 13/10

Correct? Yes

🔗 Problem

Problem: Solve the following equation for x: 66 = 9 + 10 * x

Gemma 2B:

    To solve the equation \( 66 = 9 + 10x \) for \( x \), follow these steps:

    1. Subtract 9 from both sides of the equation to isolate the term with \( x \):
       \[
       66 - 9 = 10x
       \]
       Simplifying the left side:
       \[
       57 = 10x
       \]

    2. Divide both sides by 10 to solve for \( x \):
       \[
       x = \frac{57}{10}
       \]
       Simplifying the fraction:
       \[
       x = 5.7
       \]

    ### Answer: 5.7

Expected answer: 57/10

Correct? Yes

🔗 Problem

Problem: Solve the following algebraic equation for the unknown variable a: 103 = ((38 * a) + 51)

Gemma 2B:

    To solve the equation \( 103 = 38a + 51 \) for the unknown variable \( a \), follow these steps:

    1. Subtract 51 from both sides of the equation to isolate the term with \( a \):
       \[
       103 - 51 = 38a
       \]

    2. Simplify the left side:
       \[
       52 = 38a
       \]

    3. Divide both sides by 38 to solve for \( a \):
       \[
       a = \frac{52}{38}
       \]

    4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:
       \[
       a = \frac{52 \div 2}{38 \div 2} = \frac{26}{19}
       \]

    ### Answer: \( \frac{26}{19} \)

Expected answer: 26/19

Correct? Yes

🔗 Problem

Problem: Determine the value of f in the following equation: 105 = 28 * f + 8

Gemma 2B:

    To determine the value of \( f \) in the equation \( 105 = 28f + 8 \), we need to isolate \( f \). Here are the steps:

    1. Subtract 8 from both sides of the equation:
       \[
       105 - 8 = 28f
       \]
       Simplifying the left side:
       \[
       97 = 28f
       \]

    2. Divide both sides by 28 to solve for \( f \):
       \[
       f = \frac{97}{28}
       \]

    3. Simplify the fraction if possible. In this case, 97 and 28 have no common factors other than 1, so the fraction is already in its simplest form.

    ### Answer: \( \frac{97}{28} \)

Expected answer: 97/28

Correct? Yes

🔗 Problem

Problem: Solve the linear equation for u: 12 = 63 - 50 * u

Gemma 2B:

    To solve the linear equation for \( u \):

    \[ 12 = 63 - 50u \]

    First, isolate the term with \( u \) on one side of the equation. Subtract 63 from both sides:

    \[ 12 - 63 = -50u \]

    Simplify the left side:

    \[ -51 = -50u \]

    Next, divide both sides by -50 to solve for \( u \):

    \[ u = \frac{-51}{-50} \]

    Simplify the fraction:

    \[ u = \frac{51}{50} \]

    ### Answer: \( \frac{51}{50} \)

Expected answer: 51/50

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the value of 'b': 60 = 42 + (10 * b)

Gemma 2B:

    To solve the equation \( 60 = 42 + (10 \cdot b) \) for the value of \( b \), follow these steps:

    1. Subtract 42 from both sides of the equation to isolate the term with \( b \):
       \[
       60 - 42 = 10 \cdot b
       \]

    2. Simplify the left side:
       \[
       18 = 10 \cdot b
       \]

    3. Divide both sides by 10 to solve for \( b \):
       \[
       b = \frac{18}{10}
       \]

    4. Simplify the fraction:
       \[
       b = 1.8
       \]

    ### Answer: 1.8

Expected answer: 9/5

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable 'j': 84 = ((25 * j) + 13)

Gemma 2B:

    To solve the linear equation for the variable \( j \), we start with the given equation:

    \[ 84 = 25j + 13 \]

    First, we need to isolate the term containing \( j \). We do this by subtracting 13 from both sides of the equation:

    \[ 84 - 13 = 25j \]

    Simplifying the left side:

    \[ 71 = 25j \]

    Next, we solve for \( j \) by dividing both sides of the equation by 25:

    \[ j = \frac{71}{25} \]

    Simplifying the fraction:

    \[ j = 2.84 \]

    ### Answer: 2.84

Expected answer: 71/25

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for s: 153 = 91 + 5 * s

Gemma 2B:

    To solve the linear equation \( 153 = 91 + 5s \) for \( s \), follow these steps:

    1. Subtract 91 from both sides of the equation to isolate the term with \( s \):
       \[
       153 - 91 = 5s
       \]

    2. Simplify the left side:
       \[
       62 = 5s
       \]

    3. Divide both sides by 5 to solve for \( s \):
       \[
       s = \frac{62}{5}
       \]

    4. Simplify the fraction:
       \[
       s = 12.4
       \]

    ### Answer: 12.4

Expected answer: 62/5

Correct? Yes

🔗 Problem

Problem: Solve for g in the following equation: 65 = (22 + (30 * g))

Gemma 2B:

    To solve for \( g \) in the equation \( 65 = 22 + 30g \), follow these steps:

    1. Subtract 22 from both sides of the equation to isolate the term with \( g \):
       \[
       65 - 22 = 30g
       \]
       Simplifying the left side:
       \[
       43 = 30g
       \]

    2. Divide both sides by 30 to solve for \( g \):
       \[
       g = \frac{43}{30}
       \]

    3. Simplify the fraction if possible. In this case, \( \frac{43}{30} \) is already in its simplest form.

    ### Answer: \( \frac{43}{30} \)

Expected answer: 43/30

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of f: 96 = ((29 * f) + 10)

Gemma 2B:

    To solve the linear equation for \( f \), we start with the given equation:

    \[ 96 = 29f + 10 \]

    First, we need to isolate the term containing \( f \). We do this by subtracting 10 from both sides of the equation:

    \[ 96 - 10 = 29f \]

    This simplifies to:

    \[ 86 = 29f \]

    Next, we solve for \( f \) by dividing both sides of the equation by 29:

    \[ f = \frac{86}{29} \]

    Simplifying the fraction:

    \[ f = 2.96551724137931 \]

    Since the problem does not specify the need for rounding, we can leave the answer in its exact form.

    ### Answer: 2.96551724137931

Expected answer: 86/29

Correct? No

🔗 Problem

Problem: Solve the following equation for the variable q: 80 = (19 + (14 * q))

Gemma 2B:

    To solve the equation \( 80 = 19 + 14q \) for the variable \( q \), follow these steps:

    1. Subtract 19 from both sides of the equation to isolate the term with \( q \):
       \[
       80 - 19 = 14q
       \]

    2. Simplify the left side:
       \[
       61 = 14q
       \]

    3. Divide both sides by 14 to solve for \( q \):
       \[
       q = \frac{61}{14}
       \]

    4. Simplify the fraction if possible. In this case, 61 and 14 have no common factors other than 1, so the fraction is already in its simplest form:
       \[
       q = \frac{61}{14}
       \]

    ### Answer: \( \frac{61}{14} \)

Expected answer: 61/14

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable 'm': 145 = 95 + 46 * m

Gemma 2B:

    To solve the linear equation for the variable \( m \):

    \[ 145 = 95 + 46m \]

    First, isolate the term containing \( m \) by subtracting 95 from both sides of the equation:

    \[ 145 - 95 = 46m \]

    Simplify the left side:

    \[ 50 = 46m \]

    Next, solve for \( m \) by dividing both sides by 46:

    \[ m = \frac{50}{46} \]

    Simplify the fraction:

    \[ m = \frac{25}{23} \]

    ### Answer: \(\frac{25}{23}\)

Expected answer: 25/23

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the value of 'i': 68 = 13 + 6 * i

Gemma 2B:

    To solve the equation \( 68 = 13 + 6i \) for \( i \), follow these steps:

    1. Subtract 13 from both sides of the equation to isolate the term with \( i \):
       \[
       68 - 13 = 6i
       \]
       Simplifying the left side:
       \[
       55 = 6i
       \]

    2. Divide both sides by 6 to solve for \( i \):
       \[
       i = \frac{55}{6}
       \]

    3. Simplify the fraction if possible. In this case, \( \frac{55}{6} \) is already in its simplest form.

    ### Answer: \( \frac{55}{6} \)

Expected answer: 55/6

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the value of h: 25 = ((74 * h) - 61)

Gemma 2B:

    To solve the equation \( 25 = 74h - 61 \) for \( h \), follow these steps:

    1. Start by isolating the term with \( h \) on one side of the equation. Add 61 to both sides of the equation:
       \[
       25 + 61 = 74h - 61 + 61
       \]
       Simplifying this, we get:
       \[
       86 = 74h
       \]

    2. Next, solve for \( h \) by dividing both sides of the equation by 74:
       \[
       h = \frac{86}{74}
       \]

    3. Simplify the fraction if possible:
       \[
       h = \frac{43}{37}
       \]

    ### Answer: \(\frac{43}{37}\)

Expected answer: 43/37

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of q: 51 = ((6 * q) - 30)

Gemma 2B:

    To solve the linear equation \( 51 = 6q - 30 \), we need to isolate the variable \( q \). Here are the steps:

    1. Start with the given equation:
       \[
       51 = 6q - 30
       \]

    2. Add 30 to both sides of the equation to move the constant term on the right side to the left side:
       \[
       51 + 30 = 6q - 30 + 30
       \]
       Simplifying this, we get:
       \[
       81 = 6q
       \]

    3. Divide both sides of the equation by 6 to solve for \( q \):
       \[
       \frac{81}{6} = \frac{6q}{6}
       \]
       Simplifying this, we get:
       \[
       q = 13.5
       \]

    ### Answer: 13.5

Expected answer: 27/2

Correct? Yes

🔗 Problem

Problem: Find the value of r in the following linear equation: 38 = 81 - 36 * r

Gemma 2B:

    To find the value of \( r \) in the equation \( 38 = 81 - 36r \), we need to isolate \( r \). Here are the steps:

    1. Start with the given equation:
       \[
       38 = 81 - 36r
       \]

    2. Subtract 81 from both sides to move the constant term to the left side:
       \[
       38 - 81 = -36r
       \]

    3. Simplify the left side:
       \[
       -43 = -36r
       \]

    4. Divide both sides by -36 to solve for \( r \):
       \[
       r = \frac{-43}{-36}
       \]

    5. Simplify the fraction:
       \[
       r = \frac{43}{36}
       \]

    ### Answer: \(\frac{43}{36}\)

Expected answer: 43/36

Correct? Yes

🔗 Problem

Problem: Solve the following equation: 90 = (23 + (56 * a))

Gemma 2B:

    To solve the equation \( 90 = 23 + 56a \), we need to isolate the variable \( a \).

    1. Start by subtracting 23 from both sides of the equation:
       \[
       90 - 23 = 56a
       \]
       Simplifying the left side:
       \[
       67 = 56a
       \]

    2. Next, divide both sides by 56 to solve for \( a \):
       \[
       a = \frac{67}{56}
       \]

    3. Simplify the fraction if possible:
       \[
       a = \frac{67}{56}
       \]
       Since 67 and 56 have no common factors other than 1, the fraction is already in its simplest form.

    ### Answer: \( \frac{67}{56} \)

Expected answer: 67/56

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the unknown variable h: 81 = 13 + 30 * h

Gemma 2B:

    To solve the linear equation \( 81 = 13 + 30h \) for the unknown variable \( h \), follow these steps:

    1. Subtract 13 from both sides of the equation to isolate the term with \( h \):
       \[
       81 - 13 = 30h
       \]

    2. Simplify the left side:
       \[
       68 = 30h
       \]

    3. Divide both sides by 30 to solve for \( h \):
       \[
       h = \frac{68}{30}
       \]

    4. Simplify the fraction:
       \[
       h = \frac{34}{15}
       \]

    ### Answer: \( \frac{34}{15} \)

Expected answer: 34/15

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of m: 160 = ((62 * m) + 69)

Gemma 2B:

    To solve the linear equation \( 160 = 62m + 69 \) for \( m \), follow these steps:

    1. Subtract 69 from both sides of the equation to isolate the term with \( m \):
       \[
       160 - 69 = 62m
       \]
       Simplifying the left side:
       \[
       91 = 62m
       \]

    2. Divide both sides by 62 to solve for \( m \):
       \[
       m = \frac{91}{62}
       \]

    3. Simplify the fraction if possible. In this case, 91 and 62 have no common factors other than 1, so the fraction is already in its simplest form:
       \[
       m = \frac{91}{62}
       \]

    ### Answer: \(\frac{91}{62}\)

Expected answer: 91/62

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of q: 100 = 69 + 28 * q

Gemma 2B:

    To solve the equation \( 100 = 69 + 28q \) for \( q \), follow these steps:

    1. Subtract 69 from both sides of the equation to isolate the term with \( q \):
       \[
       100 - 69 = 28q
       \]

    2. Simplify the left side:
       \[
       31 = 28q
       \]

    3. Divide both sides by 28 to solve for \( q \):
       \[
       q = \frac{31}{28}
       \]

    4. Simplify the fraction if possible. In this case, \( \frac{31}{28} \) is already in its simplest form.

    ### Answer: \(\frac{31}{28}\)

Expected answer: 31/28

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation to find the value of w: 192 = ((98 * w) + 94)

Gemma 2B:

    To solve the linear equation \( 192 = 98w + 94 \), we need to isolate the variable \( w \). Here are the steps:

    1. Subtract 94 from both sides of the equation to get rid of the constant term on the right side:
       \[
       192 - 94 = 98w
       \]

    2. Simplify the left side:
       \[
       98 = 98w
       \]

    3. Divide both sides by 98 to solve for \( w \):
       \[
       w = \frac{98}{98}
       \]

    4. Simplify the fraction:
       \[
       w = 1
       \]

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of y: 40 = 93 - 33 * y

Gemma 2B:

    To solve the equation \( 40 = 93 - 33y \) for \( y \), follow these steps:

    1. Subtract 93 from both sides of the equation to isolate the term involving \( y \):
       \[
       40 - 93 = -33y
       \]

    2. Simplify the left side:
       \[
       -53 = -33y
       \]

    3. Divide both sides by -33 to solve for \( y \):
       \[
       y = \frac{-53}{-33}
       \]

    4. Simplify the fraction:
       \[
       y = \frac{53}{33}
       \]

    ### Answer: \(\frac{53}{33}\)

Expected answer: 53/33

Correct? Yes

🔗 Problem

Problem: Solve for the unknown variable u in the following linear equation: 74 = ((48 * u) - 20)

Gemma 2B:

    To solve for the unknown variable \( u \) in the equation \( 74 = 48u - 20 \), follow these steps:

    1. Start with the given equation:
       \[
       74 = 48u - 20
       \]

    2. Add 20 to both sides of the equation to isolate the term with \( u \):
       \[
       74 + 20 = 48u
       \]

    3. Simplify the left side:
       \[
       94 = 48u
       \]

    4. Divide both sides by 48 to solve for \( u \):
       \[
       u = \frac{94}{48}
       \]

    5. Simplify the fraction by finding the greatest common divisor (GCD) of 94 and 48, which is 2:
       \[
       u = \frac{94 \div 2}{48 \div 2} = \frac{47}{24}
       \]

    ### Answer: \(\frac{47}{24}\)

Expected answer: 47/24

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the variable f: 13 = ((86 * f) - 76)

Gemma 2B:

    To solve the equation \( 13 = 86f - 76 \) for the variable \( f \), follow these steps:

    1. Add 76 to both sides of the equation to isolate the term with \( f \):
       \[
       13 + 76 = 86f - 76 + 76
       \]
       Simplifying this, we get:
       \[
       89 = 86f
       \]

    2. Divide both sides of the equation by 86 to solve for \( f \):
       \[
       f = \frac{89}{86}
       \]

    3. Simplify the fraction if possible. In this case, \( \frac{89}{86} \) is already in its simplest form.

    ### Answer: \( \frac{89}{86} \)

Expected answer: 89/86

Correct? Yes

🔗 Problem

Problem: Solve the following equation for c: 122 = (36 + (56 * c))

Gemma 2B:

    To solve the equation \( 122 = 36 + 56c \) for \( c \), follow these steps:

    1. Subtract 36 from both sides of the equation to isolate the term with \( c \):
       \[
       122 - 36 = 56c
       \]

    2. Simplify the left side:
       \[
       86 = 56c
       \]

    3. Divide both sides by 56 to solve for \( c \):
       \[
       c = \frac{86}{56}
       \]

    4. Simplify the fraction:
       \[
       c = \frac{43}{28}
       \]

    ### Answer: \( \frac{43}{28} \)

Expected answer: 43/28

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the unknown quantity q: 186 = 99 + 81 * q

Gemma 2B:

    To solve the linear equation for the unknown quantity \( q \), we start with the given equation:

    \[ 186 = 99 + 81q \]

    First, we need to isolate the term containing \( q \). We do this by subtracting 99 from both sides of the equation:

    \[ 186 - 99 = 81q \]

    Simplifying the left side:

    \[ 87 = 81q \]

    Next, we solve for \( q \) by dividing both sides of the equation by 81:

    \[ q = \frac{87}{81} \]

    Simplifying the fraction:

    \[ q = \frac{87 \div 3}{81 \div 3} = \frac{29}{27} \]

    Thus, the value of \( q \) is:

    ### Answer: \(\frac{29}{27}\)

Expected answer: 29/27

Correct? Yes

🔗 Problem

Problem: Find the value of 'u' in the following equation: 120 = ((42 * u) + 77)

Gemma 2B:

    To find the value of \( u \) in the equation \( 120 = (42u + 77) \), we need to isolate \( u \). Here are the steps:

    1. Start with the given equation:
       \[
       120 = 42u + 77
       \]

    2. Subtract 77 from both sides to isolate the term with \( u \):
       \[
       120 - 77 = 42u
       \]

    3. Simplify the left side:
       \[
       43 = 42u
       \]

    4. Divide both sides by 42 to solve for \( u \):
       \[
       u = \frac{43}{42}
       \]

    ### Answer: \(\frac{43}{42}\)

Expected answer: 43/42

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of j: 103 = (52 + (6 * j))

Gemma 2B:

    To solve the equation \( 103 = 52 + (6 \cdot j) \), we need to isolate the variable \( j \). Here are the steps:

    1. Start with the given equation:
       \[
       103 = 52 + (6 \cdot j)
       \]

    2. Subtract 52 from both sides to isolate the term with \( j \):
       \[
       103 - 52 = 6 \cdot j
       \]

    3. Simplify the left side:
       \[
       51 = 6 \cdot j
       \]

    4. Divide both sides by 6 to solve for \( j \):
       \[
       j = \frac{51}{6}
       \]

    5. Simplify the fraction:
       \[
       j = 8.5
       \]

    ### Answer: 8.5

Expected answer: 17/2

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of n: 56 = (82 - (4 * n))

Gemma 2B:

    To solve the linear equation \( 56 = 82 - 4n \), we need to isolate the variable \( n \). Here are the steps:

    1. Start with the given equation:
       \[
       56 = 82 - 4n
       \]

    2. Subtract 82 from both sides to isolate the term involving \( n \):
       \[
       56 - 82 = -4n
       \]

    3. Simplify the left side:
       \[
       -26 = -4n
       \]

    4. Divide both sides by -4 to solve for \( n \):
       \[
       n = \frac{-26}{-4}
       \]

    5. Simplify the fraction:
       \[
       n = \frac{26}{4} = 6.5
       \]

    ### Answer: 6.5

Expected answer: 13/2

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for m: 77 = 14 + 60 * m

Gemma 2B:

    To solve the linear equation \( 77 = 14 + 60m \) for \( m \), follow these steps:

    1. Subtract 14 from both sides of the equation to isolate the term with \( m \):
       \[
       77 - 14 = 60m
       \]

    2. Simplify the left side:
       \[
       63 = 60m
       \]

    3. Divide both sides by 60 to solve for \( m \):
       \[
       m = \frac{63}{60}
       \]

    4. Simplify the fraction:
       \[
       m = \frac{21}{20}
       \]

    ### Answer: \( \frac{21}{20} \)

Expected answer: 21/20

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable 'e': 31 = 17 + e

Gemma 2B:

    To solve the linear equation for the variable \( e \), we need to isolate \( e \) on one side of the equation. Here are the steps:

    1. Start with the given equation:
       \[
       31 = 17 + e
       \]

    2. Subtract 17 from both sides of the equation to isolate \( e \):
       \[
       31 - 17 = e
       \]

    3. Simplify the left side:
       \[
       14 = e
       \]

    Thus, the value of \( e \) is 14.

    ### Answer: 14

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: Find the value of x that solves the following equation: 2 = 81 - (15 * x)

Gemma 2B:

    To find the value of \( x \) that solves the equation \( 2 = 81 - 15x \), we need to isolate \( x \). Here are the steps:

    1. Start with the given equation:
       \[
       2 = 81 - 15x
       \]

    2. Subtract 81 from both sides to move the constant term to the left side:
       \[
       2 - 81 = -15x
       \]

    3. Simplify the left side:
       \[
       -79 = -15x
       \]

    4. Divide both sides by -15 to solve for \( x \):
       \[
       x = \frac{-79}{-15}
       \]

    5. Simplify the fraction:
       \[
       x = \frac{79}{15}
       \]

    ### Answer: \(\frac{79}{15}\)

Expected answer: 79/15

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the value of e: 177 = 88 + 6 * e.

Gemma 2B:

    To solve the equation \( 177 = 88 + 6e \) for \( e \), follow these steps:

    1. Subtract 88 from both sides of the equation to isolate the term with \( e \):
       \[
       177 - 88 = 6e
       \]

    2. Simplify the left side:
       \[
       89 = 6e
       \]

    3. Divide both sides by 6 to solve for \( e \):
       \[
       e = \frac{89}{6}
       \]

    4. Simplify the fraction if possible:
       \[
       e = 14.8333\ldots \quad \text{(or as a fraction, } \frac{89}{6} \text{)}
       \]

    ### Answer: \( \frac{89}{6} \) or approximately 14.8333

Expected answer: 89/6

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of 'r': 95 = 3*r + 15

Gemma 2B:

    To solve the equation \( 95 = 3r + 15 \), we need to isolate the variable \( r \). Here are the steps:

    1. Subtract 15 from both sides of the equation to get rid of the constant term on the right side:
       \[
       95 - 15 = 3r + 15 - 15
       \]
       Simplifying this, we get:
       \[
       80 = 3r
       \]

    2. Next, divide both sides of the equation by 3 to solve for \( r \):
       \[
       \frac{80}{3} = \frac{3r}{3}
       \]
       Simplifying this, we get:
       \[
       r = \frac{80}{3}
       \]

    ### Answer: \(\frac{80}{3}\)

Expected answer: 80/3

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of v: 154 = (70 + (31 * v))

Gemma 2B:

    To solve the linear equation \( 154 = 70 + 31v \) for \( v \), follow these steps:

    1. Subtract 70 from both sides of the equation to isolate the term with \( v \):
       \[
       154 - 70 = 31v
       \]
       Simplifying the left side:
       \[
       84 = 31v
       \]

    2. Divide both sides by 31 to solve for \( v \):
       \[
       v = \frac{84}{31}
       \]

    3. Simplify the fraction if possible:
       \[
       v = \frac{84}{31}
       \]

    Since 84 and 31 have no common factors other than 1, the fraction is already in its simplest form.

    ### Answer: \( v = \frac{84}{31} \)

Expected answer: 84/31

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the value of r: 179 = ((70 * r) + 87)

Gemma 2B:

    To solve the equation \( 179 = 70r + 87 \) for \( r \), follow these steps:

    1. Subtract 87 from both sides of the equation to isolate the term with \( r \):
       \[
       179 - 87 = 70r
       \]

    2. Simplify the left side:
       \[
       92 = 70r
       \]

    3. Divide both sides by 70 to solve for \( r \):
       \[
       r = \frac{92}{70}
       \]

    4. Simplify the fraction:
       \[
       r = \frac{46}{35}
       \]

    Thus, the value of \( r \) is:
    ### Answer: \(\frac{46}{35}\)

Expected answer: 46/35

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of r: 93 = ((19 * r) + 2)

Gemma 2B:

    To solve the equation \( 93 = (19r + 2) \) for \( r \), follow these steps:

    1. Subtract 2 from both sides of the equation to isolate the term with \( r \):
       \[
       93 - 2 = 19r
       \]
       Simplifying the left side:
       \[
       91 = 19r
       \]

    2. Divide both sides by 19 to solve for \( r \):
       \[
       r = \frac{91}{19}
       \]
       Simplifying the fraction:
       \[
       r = 4.789
       \]

    ### Answer: 4.789

Expected answer: 91/19

Correct? No

🔗 Problem

Problem: Solve the following linear equation for the value of z: 20 = (67 - (37 * z))

Gemma 2B:

    To solve the linear equation \( 20 = 67 - 37z \), we need to isolate the variable \( z \). Here are the steps:

    1. Start with the given equation:
       \[
       20 = 67 - 37z
       \]

    2. Subtract 67 from both sides to move the constant term to the left side:
       \[
       20 - 67 = -37z
       \]

    3. Simplify the left side:
       \[
       -47 = -37z
       \]

    4. Divide both sides by -37 to solve for \( z \):
       \[
       z = \frac{-47}{-37}
       \]

    5. Simplify the fraction:
       \[
       z = \frac{47}{37}
       \]

    ### Answer: \( \frac{47}{37} \)

Expected answer: 47/37

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for m: 65 = ((25 * m) + 15)

Gemma 2B:

    To solve the linear equation for \( m \):

    \[ 65 = 25m + 15 \]

    First, isolate the term with \( m \) by subtracting 15 from both sides of the equation:

    \[ 65 - 15 = 25m \]

    This simplifies to:

    \[ 50 = 25m \]

    Next, solve for \( m \) by dividing both sides by 25:

    \[ m = \frac{50}{25} \]

    This simplifies to:

    \[ m = 2 \]

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for g: 79 = ((6 * g) + 19)

Gemma 2B:

    To solve the linear equation \( 79 = 6g + 19 \) for \( g \), follow these steps:

    1. Subtract 19 from both sides of the equation to isolate the term with \( g \):
       \[
       79 - 19 = 6g
       \]
       Simplifying the left side:
       \[
       60 = 6g
       \]

    2. Divide both sides by 6 to solve for \( g \):
       \[
       \frac{60}{6} = g
       \]
       Simplifying the right side:
       \[
       g = 10
       \]

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable 'l': 30 = ((56 * l) - 45)

Gemma 2B:

    To solve the linear equation \( 30 = 56l - 45 \) for the variable \( l \), follow these steps:

    1. Start by isolating the term containing \( l \). Add 45 to both sides of the equation:
       \[
       30 + 45 = 56l - 45 + 45
       \]
       Simplifying the left side:
       \[
       75 = 56l
       \]

    2. Next, solve for \( l \) by dividing both sides of the equation by 56:
       \[
       l = \frac{75}{56}
       \]

    3. Simplify the fraction if possible. In this case, 75 and 56 have no common factors other than 1, so the fraction is already in its simplest form:
       \[
       l = \frac{75}{56}
       \]

    ### Answer: \(\frac{75}{56}\)

Expected answer: 75/56

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of j: 57 = ((11 * j) + 4)

Gemma 2B:

    To solve the equation \( 57 = 11j + 4 \) for \( j \), follow these steps:

    1. Subtract 4 from both sides of the equation to isolate the term with \( j \):
       \[
       57 - 4 = 11j
       \]
       \[
       53 = 11j
       \]

    2. Divide both sides by 11 to solve for \( j \):
       \[
       j = \frac{53}{11}
       \]

    3. Simplify the fraction if possible:
       \[
       j = 4.8181\ldots \approx 4.818
       \]

    ### Answer: 4.818

Expected answer: 53/11

Correct? No

🔗 Problem

Problem: Solve the following equation to find the value of 'f': 36 = 34 * f - 56

Gemma 2B:

    To solve the equation \( 36 = 34f - 56 \) for \( f \), follow these steps:

    1. Add 56 to both sides of the equation to isolate the term with \( f \) on one side:
       \[
       36 + 56 = 34f - 56 + 56
       \]
       Simplifying this, we get:
       \[
       92 = 34f
       \]

    2. Divide both sides of the equation by 34 to solve for \( f \):
       \[
       f = \frac{92}{34}
       \]

    3. Simplify the fraction:
       \[
       f = \frac{92}{34} = \frac{46}{17} = 2.7
       \]

    ### Answer: 2.7

Expected answer: 46/17

Correct? No

🔗 Problem

Problem: Solve the following linear equation to find the value of 'u': 56 = (70 * u) - 43

Gemma 2B:

    To solve the linear equation \( 56 = 70u - 43 \), we need to isolate the variable \( u \). Here are the steps:

    1. Start with the given equation:
       \[
       56 = 70u - 43
       \]

    2. Add 43 to both sides of the equation to move the constant term on the right side to the left side:
       \[
       56 + 43 = 70u
       \]

    3. Simplify the left side:
       \[
       99 = 70u
       \]

    4. Divide both sides by 70 to solve for \( u \):
       \[
       u = \frac{99}{70}
       \]

    5. Simplify the fraction if possible:
       \[
       u = \frac{99}{70} = 1.4142857142857143 \approx 1.414
       \]

    ### Answer: \( \frac{99}{70} \) or approximately 1.414

Expected answer: 99/70

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the variable x: 67 = 21 + 9*x

Gemma 2B:

    To solve the equation \( 67 = 21 + 9x \) for the variable \( x \), follow these steps:

    1. Subtract 21 from both sides of the equation to isolate the term with \( x \):
       \[
       67 - 21 = 9x
       \]

    2. Simplify the left side:
       \[
       46 = 9x
       \]

    3. Divide both sides by 9 to solve for \( x \):
       \[
       x = \frac{46}{9}
       \]

    4. Simplify the fraction if possible. In this case, \(\frac{46}{9}\) is already in its simplest form.

    ### Answer: \( \frac{46}{9} \)

Expected answer: 46/9

Correct? Yes

🔗 Problem

Problem: Determine the unknown variable in the following equation: 75 = (58 + 16 * i)

Gemma 2B:

    To determine the unknown variable \( i \) in the equation \( 75 = 58 + 16i \), we need to isolate \( i \).

    First, subtract 58 from both sides of the equation:
    \[ 75 - 58 = 16i \]

    Simplify the left side:
    \[ 17 = 16i \]

    Next, divide both sides by 16 to solve for \( i \):
    \[ i = \frac{17}{16} \]

    ### Answer: \(\frac{17}{16}\)

Expected answer: 17/16

Correct? Yes

🔗 Problem

Problem: Solve for x in the following equation: 111 = (54 + (39 * x))

Gemma 2B:

    To solve for \( x \) in the equation \( 111 = 54 + 39x \), follow these steps:

    1. Subtract 54 from both sides of the equation to isolate the term with \( x \):
       \[
       111 - 54 = 39x
       \]

    2. Simplify the left side:
       \[
       57 = 39x
       \]

    3. Divide both sides by 39 to solve for \( x \):
       \[
       x = \frac{57}{39}
       \]

    4. Simplify the fraction:
       \[
       x = \frac{57 \div 3}{39 \div 3} = \frac{19}{13}
       \]

    ### Answer: \( \frac{19}{13} \)

Expected answer: 19/13

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of 'o': 155 = ((26 * o) + 68)

Gemma 2B:

    To solve the equation \( 155 = 26o + 68 \) for \( o \), follow these steps:

    1. Subtract 68 from both sides of the equation to isolate the term with \( o \):
       \[
       155 - 68 = 26o
       \]

    2. Calculate the left-hand side:
       \[
       87 = 26o
       \]

    3. Divide both sides by 26 to solve for \( o \):
       \[
       o = \frac{87}{26}
       \]

    4. Simplify the fraction:
       \[
       o = \frac{87}{26} = 3.346153846153846
       \]

    ### Answer: 3.346153846153846

Expected answer: 87/26

Correct? No

🔗 Problem

Problem: Solve for p in the following equation: 7 = ((12 * p) - 17)

Gemma 2B:

    To solve for \( p \) in the equation \( 7 = 12p - 17 \), follow these steps:

    1. Start with the given equation:
       \[
       7 = 12p - 17
       \]

    2. Add 17 to both sides of the equation to isolate the term with \( p \):
       \[
       7 + 17 = 12p - 17 + 17
       \]
       Simplifying the left side:
       \[
       24 = 12p
       \]

    3. Divide both sides by 12 to solve for \( p \):
       \[
       \frac{24}{12} = \frac{12p}{12}
       \]
       Simplifying both sides:
       \[
       2 = p
       \]

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: Solve the following problem: What is the value of the variable 'b' if 163 = 93 + 55 * b?

Gemma 2B:

    To find the value of the variable \( b \) in the equation \( 163 = 93 + 55b \), we need to isolate \( b \). Here are the steps:

    1. Start with the given equation:
       \[
       163 = 93 + 55b
       \]

    2. Subtract 93 from both sides to isolate the term with \( b \):
       \[
       163 - 93 = 55b
       \]

    3. Simplify the left side:
       \[
       70 = 55b
       \]

    4. Divide both sides by 55 to solve for \( b \):
       \[
       b = \frac{70}{55}
       \]

    5. Simplify the fraction:
       \[
       b = \frac{14}{11}
       \]

    ### Answer: \(\frac{14}{11}\)

Expected answer: 14/11

Correct? Yes

🔗 Problem

Problem: Solve the linear equation for the value of 'u': 62 = (u - 26)

Gemma 2B:

    To solve the linear equation for the value of \( u \), we start with the given equation:

    \[ 62 = u - 26 \]

    To isolate \( u \), we need to get rid of the \(-26\) on the right side. We do this by adding 26 to both sides of the equation:

    \[ 62 + 26 = u - 26 + 26 \]

    Simplifying both sides, we get:

    \[ 88 = u \]

    Thus, the value of \( u \) is:

    ### Answer: 88

Expected answer: 88

Correct? Yes

🔗 Problem

Problem: Solve the following equation for the variable a: 179 = ((63 * a) + 93)

Gemma 2B:

    To solve the equation for the variable \( a \):

    \[ 179 = 63a + 93 \]

    First, isolate the term containing \( a \) by subtracting 93 from both sides of the equation:

    \[ 179 - 93 = 63a \]

    Simplify the left side:

    \[ 86 = 63a \]

    Next, solve for \( a \) by dividing both sides by 63:

    \[ a = \frac{86}{63} \]

    Simplify the fraction if possible:

    \[ a = \frac{86}{63} \]

    Since 86 and 63 have no common factors other than 1, the fraction is already in its simplest form.

    ### Answer: \( \frac{86}{63} \)

Expected answer: 86/63

Correct? Yes

🔗 Problem

Problem: Find the value of c in the equation: 51 = ((27 * c) - 11)

Gemma 2B:

    To find the value of \( c \) in the equation \( 51 = (27c - 11) \), we need to isolate \( c \). Here are the steps:

    1. Start with the given equation:
       \[
       51 = 27c - 11
       \]

    2. Add 11 to both sides to move the constant term on the right side to the left side:
       \[
       51 + 11 = 27c
       \]

    3. Simplify the left side:
       \[
       62 = 27c
       \]

    4. Divide both sides by 27 to solve for \( c \):
       \[
       c = \frac{62}{27}
       \]

    5. Simplify the fraction if possible. In this case, \( \frac{62}{27} \) is already in its simplest form.

    ### Answer: \(\frac{62}{27}\)

Expected answer: 62/27

Correct? Yes

🔗 Problem

Problem: Solve the following equation for 'd': 19 = ((28 * d) - 18)

Gemma 2B:

    To solve the equation for \( d \), we start with the given equation:

    \[ 19 = (28d - 18) \]

    First, we need to isolate the term containing \( d \). We do this by adding 18 to both sides of the equation:

    \[ 19 + 18 = 28d \]

    Simplifying the left side:

    \[ 37 = 28d \]

    Next, we solve for \( d \) by dividing both sides by 28:

    \[ d = \frac{37}{28} \]

    Simplifying the fraction, we get:

    \[ d = \frac{37}{28} \]

    ### Answer: \(\frac{37}{28}\)

Expected answer: 37/28

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of e: 159 = ((47 * e) + 62)

Gemma 2B:

    To solve the linear equation \( 159 = 47e + 62 \) for \( e \), follow these steps:

    1. Subtract 62 from both sides of the equation to isolate the term with \( e \):
       \[
       159 - 62 = 47e
       \]

    2. Simplify the left side:
       \[
       97 = 47e
       \]

    3. Divide both sides by 47 to solve for \( e \):
       \[
       e = \frac{97}{47}
       \]

    4. Simplify the fraction if possible. In this case, 97 and 47 are both prime numbers, so the fraction is already in its simplest form:
       \[
       e = \frac{97}{47}
       \]

    ### Answer: \(\frac{97}{47}\)

Expected answer: 97/47

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable g: 145 = (50 + (91 * g))

Gemma 2B:

    To solve the linear equation for the variable \( g \):

    \[ 145 = 50 + 91g \]

    First, isolate the term containing \( g \) by subtracting 50 from both sides of the equation:

    \[ 145 - 50 = 91g \]

    This simplifies to:

    \[ 95 = 91g \]

    Next, solve for \( g \) by dividing both sides of the equation by 91:

    \[ g = \frac{95}{91} \]

    Simplify the fraction if possible:

    \[ g = \frac{95}{91} = \frac{95 \div 5}{91 \div 5} = \frac{19}{18.2} \]

    Since 95 and 91 do not have a common factor other than 1, the fraction is already in its simplest form.

    ### Answer: \(\frac{95}{91}\)

Expected answer: 95/91

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the value of l: 123 = ((44 * l) + 73)

Gemma 2B:

    To solve the linear equation \( 123 = 44l + 73 \) for \( l \), follow these steps:

    1. Subtract 73 from both sides of the equation to isolate the term with \( l \):
       \[
       123 - 73 = 44l
       \]

    2. Simplify the left side:
       \[
       50 = 44l
       \]

    3. Divide both sides by 44 to solve for \( l \):
       \[
       l = \frac{50}{44}
       \]

    4. Simplify the fraction:
       \[
       l = \frac{25}{22}
       \]

    ### Answer: \(\frac{25}{22}\)

Expected answer: 25/22

Correct? Yes

🔗 Problem

Problem: Solve the following equation: 165 = ((19 * q) + 75)

Gemma 2B:

    To solve the equation \( 165 = 19q + 75 \), we need to isolate the variable \( q \).

    1. Subtract 75 from both sides of the equation:
       \[
       165 - 75 = 19q
       \]
       Simplifying the left side:
       \[
       90 = 19q
       \]

    2. Divide both sides by 19 to solve for \( q \):
       \[
       q = \frac{90}{19}
       \]

    3. Simplify the fraction:
       \[
       q = \frac{90}{19} \approx 4.7368
       \]

    ### Answer: \( \frac{90}{19} \) or approximately 4.7368

Expected answer: 90/19

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation to find the value of g: 149 = ((18 * g) + 62)

Gemma 2B:

    To solve the linear equation \( 149 = 18g + 62 \), we need to isolate the variable \( g \). Here are the steps:

    1. Subtract 62 from both sides of the equation to get rid of the constant term on the right side:
       \[
       149 - 62 = 18g
       \]

    2. Simplify the left side:
       \[
       87 = 18g
       \]

    3. Divide both sides by 18 to solve for \( g \):
       \[
       g = \frac{87}{18}
       \]

    4. Simplify the fraction:
       \[
       g = \frac{87 \div 3}{18 \div 3} = \frac{29}{6}
       \]

    So, the value of \( g \) is:
    ### Answer: \(\frac{29}{6}\)

Expected answer: 29/6

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the variable d: 84 = 20 * d + 21

Gemma 2B:

    To solve the linear equation \( 84 = 20d + 21 \) for the variable \( d \), follow these steps:

    1. Subtract 21 from both sides of the equation to isolate the term with \( d \):
       \[
       84 - 21 = 20d + 21 - 21
       \]
       Simplifying this, we get:
       \[
       63 = 20d
       \]

    2. Divide both sides of the equation by 20 to solve for \( d \):
       \[
       \frac{63}{20} = d
       \]

    Thus, the value of \( d \) is:
    ### Answer: \(\frac{63}{20}\)

Expected answer: 63/20

Correct? Yes

🔗 Problem

Problem: Solve the following equation to find the value of g: 61 = (50 + (6 * g))

Gemma 2B:

    To solve the equation \( 61 = 50 + 6g \), we need to isolate the variable \( g \).

    1. Start by subtracting 50 from both sides of the equation:
       \[
       61 - 50 = 50 + 6g - 50
       \]
       Simplifying this, we get:
       \[
       11 = 6g
       \]

    2. Next, divide both sides by 6 to solve for \( g \):
       \[
       \frac{11}{6} = g
       \]

    So, the value of \( g \) is:
    ### Answer: \(\frac{11}{6}\)

Expected answer: 11/6

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for the unknown variable v: 126 = ((21 * v) + 76)

Gemma 2B:

    To solve the linear equation for the unknown variable \( v \), we start with the given equation:

    \[ 126 = 21v + 76 \]

    First, we need to isolate the term containing \( v \). We do this by subtracting 76 from both sides of the equation:

    \[ 126 - 76 = 21v \]

    Simplifying the left side:

    \[ 50 = 21v \]

    Next, we solve for \( v \) by dividing both sides of the equation by 21:

    \[ v = \frac{50}{21} \]

    Thus, the value of \( v \) is:

    ### Answer: \(\frac{50}{21}\)

Expected answer: 50/21

Correct? Yes

🔗 Problem

Problem: Solve the following linear equation for g: 74 = ((91 * g) - 24)

Gemma 2B:

    To solve the linear equation for \( g \), we start with the given equation:

    \[ 74 = 91g - 24 \]

    First, we need to isolate the term containing \( g \). We do this by adding 24 to both sides of the equation:

    \[ 74 + 24 = 91g - 24 + 24 \]

    This simplifies to:

    \[ 98 = 91g \]

    Next, we solve for \( g \) by dividing both sides of the equation by 91:

    \[ g = \frac{98}{91} \]

    Simplify the fraction:

    \[ g = \frac{98 \div 7}{91 \div 7} = \frac{14}{13} \]

    ### Answer: \(\frac{14}{13}\)

Expected answer: 14/13

Correct? Yes