Common Core Standard 8.EE.C.7
This standard covers the following:
Solve linear equations in one variable.
Problem: Solve the following equation for the variable u: 122 = 92 + 28 * u
Gemma 2B:
To solve the equation 122 = 92 + 28u for u, we first subtract 92 from both sides to isolate the term with u: 122 - 92 = 92 + 28u - 92, 30 = 28u. Next, we divide both sides by 28 to solve for u: 30/28 = (28u)/28, u = 30/28. Therefore, u = 15/14. ### Answer: u = 15/14.
Expected answer: 15/14
Correct? Yes
Problem: Solve the following equation for i: 42 = ((35 * i) - 34)
Gemma 2B:
To solve for \( i \), we first isolate the term with \( i \) by moving the constant term to the other side of the equation:
\( 42 = 35i - 34 \)
Adding 34 to both sides gives:
\( 42 + 34 = 35i \)
\( 76 = 35i \)
Finally, divide by 35 to solve for \( i \):
\( i = \frac{76}{35} \)
### Answer: \( i = \frac{76}{35} \)
Expected answer: 76/35
Correct? Yes
Problem: Solve the following equation to find the value of r: 94 = 41 + 6 * r
Gemma 2B:
To solve the equation 94 = 41 + 6r, we first subtract 41 from both sides to isolate the term with r: 94 - 41 = 41 - 41 + 6r 53 = 6r Next, we divide both sides by 6 to solve for r: r = 53/6 r = 8.83 ### Answer: r = 8.83
Expected answer: 53/6
Correct? No
Problem: Determine the value of "i" from the following equation: 158 = ((19 * i) + 94)
Gemma 2B:
To find the value of \( i \), we need to isolate \( i \) in the equation.
Given: \( 158 = 19i + 94 \)
Subtract 94 from both sides:
\( 158 - 94 = 19i \)
\( 64 = 19i \)
Divide by 19 on both sides:
\( i = \frac{64}{19} \)
Therefore, \( i = \frac{64}{19} \) or approximately \( i \approx 3.3684 \).
### Answer: \( i = \frac{64}{19} \) or approximately \( i \approx 3.3684 \).
Expected answer: 64/19
Correct? Yes
Problem: Solve the following equation for 'q': 134 = ((30 * q) + 54)
Gemma 2B:
First, we need to isolate 'q' by performing the inverse operations. 1. Subtract 54 from both sides: 134 - 54 = 30q 80 = 30q 2. Divide by 30 on both sides to solve for 'q': 80/30 = q q = 2.67 ### Answer: q = 2.67
Expected answer: 8/3
Correct? No
Problem: Solve the following linear equation to find the value of y: 94 = (27 + y)
Gemma 2B:
To solve the equation 94 = 27 + y for y, we need to isolate y by subtracting 27 from both sides: 94 - 27 = 27 + y - 27, 67 = y. Therefore, the value of y is y = 67. ### Answer: y = 67
Expected answer: 67
Correct? Yes
Problem: Solve the following linear equation for the value of h: 9 = ((23 * h) - 70)
Gemma 2B:
To solve the equation 9 = 23h - 70 for h, we first isolate the term with h by adding 70 to both sides: 9 + 70 = 23h 79 = 23h Next, we divide both sides by 23 to solve for h: h = 79/23 h = 3.4347826087 (rounded to 10 decimal places) ### Answer: h = 3.4347826087.
Expected answer: 79/23
Correct? No
Problem: Solve the following equation to find the value of t: 92 = 33 * t + 26
Gemma 2B:
To solve for \( t \), we need to isolate \( t \) on one side of the equation.
First, we subtract 26 from both sides of the equation:
\( 92 - 26 = 33t \)
\( 66 = 33t \)
Next, we divide both sides by 33 to solve for \( t \):
\( t = \frac{66}{33} \)
\( t = 2 \)
### Answer: \( t = 2 \)
Expected answer: 2
Correct? Yes
Problem: Solve the following linear equation to find the value of e: 123 = ((15 * e) + 29).
Gemma 2B:
To solve the equation 123 = 15e + 29 for e, we first isolate the term with e by subtracting 29 from both sides: 123 - 29 = 15e 94 = 15e Next, we divide both sides by 15 to solve for e: e = 94/15 e = 6.27 ### Answer: e = 6.27
Expected answer: 94/15
Correct? No
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, we first add 80 to both sides to isolate the term with k: 16 + 80 = 75k - 80 + 80 96 = 75k Next, we divide both sides by 75 to solve for k: k = 96/75 k = 1.28 ### Answer: k = 1.28
Expected answer: 32/25
Correct? Yes
Problem: Solve for q in the following equation: 131 = ((5 * q) + 89)
Gemma 2B:
To solve for \( q \), we first isolate the term with \( q \) by subtracting 89 from both sides:
\( 131 - 89 = 5q \)
\( 42 = 5q \)
Next, we divide both sides by 5 to solve for \( q \):
\( q = \frac{42}{5} \)
\( q = 8.4 \)
### Answer: \( q = 8.4 \)
Expected answer: 42/5
Correct? Yes
Problem: Find the value of p that satisfies the following equation: 147 = ((38 * p) + 56)
Gemma 2B:
Reasoning: To find the value of \( p \), we need to isolate \( p \) in the equation.
\( 147 = 38p + 56 \)
Subtract 56 from both sides:
\( 147 - 56 = 38p \)
\( 91 = 38p \)
Divide by 38 on both sides:
\( p = \frac{91}{38} \)
### Answer: \( p = \frac{91}{38} \)
Expected answer: 91/38
Correct? Yes
Problem: Solve the following equation to find the value of 'j': 76 = 42 * j + 23
Gemma 2B:
To solve for 'j', we need to isolate 'j' on one side of the equation. First, we subtract 23 from both sides of the equation: 76 - 23 = 42j 53 = 42j Next, we divide both sides by 42 to solve for 'j': j = 53/42 j = 1.2619 (rounded to four decimal places) ### Answer: j = 1.2619.
Expected answer: 53/42
Correct? No
Problem: Solve the following equation to find the value of 'l': 138 = 43 + 25 * l
Gemma 2B:
To solve for 'l', we first isolate 'l' by subtracting 43 from both sides: 138 - 43 = 43 + 25 * l - 43 95 = 25 * l Next, we divide both sides by 25 to solve for 'l': l = 95 / 25 l = 3.8 ### Answer: l = 3.8
Expected answer: 19/5
Correct? Yes
Problem: Solve the following equation to find the unknown w: 80 = ((24 * w) + 35)
Gemma 2B:
First, we need to isolate the variable w by subtracting 35 from both sides of the equation: 80 - 35 = 24w 45 = 24w Next, we divide both sides by 24 to solve for w: 45/24 = w w = 1.875 ### Answer: w = 1.875
Expected answer: 15/8
Correct? Yes
Problem: Solve the following linear equation to find the value of x: 77 = (33 + (14 * x))
Gemma 2B:
First, we simplify the equation by performing the multiplication inside the parentheses: 33 + (14 * x) = 33 + 14x Now, we substitute this back into the original equation: 77 = 33 + 14x Next, we isolate the variable by subtracting 33 from both sides: 77 - 33 = 33 - 33 + 14x 44 = 14x Finally, we solve for x by dividing both sides by 14: x = 44/14 x = 3.143 ### Answer: x = 3.143
Expected answer: 22/7
Correct? No
Problem: Solve the following linear equation to find the value of y: 110 = 12 + 88 * y
Gemma 2B:
First, we need to isolate the variable y by subtracting 12 from both sides of the equation: 110 - 12 = 12 + 88y - 12, 98 = 88y. Next, we divide both sides by 88 to solve for y: y = 98/88, y = 1.1136. ### Answer: y = 1.1136.
Expected answer: 49/44
Correct? No
Problem: Solve the following linear equation for the variable 's': 179 = 82 * s + 80
Gemma 2B:
To solve the equation 179 = 82s + 80 for s, we first isolate the term with s by subtracting 80 from both sides: 179 - 80 = 82s + 80 - 80, 99 = 82s. Next, we isolate s by dividing both sides by 82: 99/82 = 82s/82, s = 99/82. Therefore, s = 99/82. ### Answer: s = 99/82.
Expected answer: 99/82
Correct? Yes
Problem: Solve the following equation for m: 129 = 26 * m + 66
Gemma 2B:
To solve for \(m\), we need to isolate \(m\) on one side of the equation.
Given equation: \(129 = 26m + 66\)
Subtract 66 from both sides:
\(129 - 66 = 26m\)
\(63 = 26m\)
Divide by 26 on both sides:
\(\frac{63}{26} = m\)
So, \(m = \frac{63}{26}\).
### Answer: \(m = \frac{63}{26}\)
Expected answer: 63/26
Correct? Yes
Problem: Solve the following linear equation for q: 82 = ((27 * q) - 17)
Gemma 2B:
To solve the equation 82 = 27q - 17 for q, we first isolate the term with q by adding 17 to both sides: 82 + 17 = 27q 99 = 27q Next, we divide both sides by 27 to solve for q: 99/27 = q q = 3 ### Answer: q = 3
Expected answer: 11/3
Correct? No
Problem: Solve the following linear equation for the variable k: 141 = (64 + (22 * k))
Gemma 2B:
To solve the equation 141 = 64 + 22k for k, we first need to isolate the variable k. Subtract 64 from both sides: 141 - 64 = 64 + 22k - 64 77 = 22k Divide both sides by 22 to solve for k: 77/22 = 22k/22 k = 77/22 Therefore, k = 3.5. ### Answer: k = 3.5.
Expected answer: 7/2
Correct? Yes
Problem: Determine the value of 'v' by solving this linear equation: 175 = 91 + 45 * v
Gemma 2B:
First, we need to isolate the variable 'v' by performing the necessary operations to solve for it. Subtract 91 from both sides of the equation: 175 - 91 = 91 - 91 + 45v 84 = 45v Divide both sides by 45 to solve for 'v': 84/45 = 45v/45 v = 1.86666666667 ### Answer: v = 1.86666666667
Expected answer: 28/15
Correct? No
Problem: Solve the following equation for the value of k: 50 = ((63 * k) - 18)
Gemma 2B:
To solve for \( k \), we first isolate the term with \( k \) by moving the constant term to the other side of the equation:
\( 50 = 63k - 18 \)
Adding 18 to both sides:
\( 50 + 18 = 63k \)
\( 68 = 63k \)
Dividing by 63:
\( k = \frac{68}{63} \)
Therefore, \( k = \frac{68}{63} \) or approximately \( k \approx 1.0794 \).
### Answer: \( k = \frac{68}{63} \) or approximately \( k \approx 1.0794 \).
Expected answer: 68/63
Correct? Yes
Problem: Solve the following equation for l: 65 = ((8 * l) - 10)
Gemma 2B:
To solve for \( l \), we first isolate the term with \( l \) by moving the constant term to the other side of the equation:
\( 65 = 8l - 10 \)
Add 10 to both sides:
\( 65 + 10 = 8l \)
\( 75 = 8l \)
Divide by 8:
\( l = \frac{75}{8} \)
\( l = 9.375 \)
### Answer: \( l = 9.375 \)
Expected answer: 75/8
Correct? Yes
Problem: Solve the following equation: 5 = ((10 * u) - 34)
Gemma 2B:
To solve the equation, we first isolate the variable u by adding 34 to both sides and then dividing by 10: 5 + 34 = 10u 39 = 10u u = 39/10 u = 3.9 ### Answer: u = 3.9
Expected answer: 39/10
Correct? Yes
Problem: Solve the following problem in linear equations for variable 'a': 91 = 9 * a + 61
Gemma 2B:
To solve for variable 'a', we need to isolate 'a' on one side of the equation. Given equation: 91 = 9a + 61 Subtract 61 from both sides: 91 - 61 = 9a 30 = 9a Divide by 9 on both sides to solve for 'a': 30/9 = a a = 10 ### Answer: a = 10
Expected answer: 10/3
Correct? No
Problem: Solve the following linear equation for the variable i: 157 = 53 * i + 61
Gemma 2B:
To solve for \(i\), we need to isolate \(i\) on one side of the equation.
First, we subtract 61 from both sides of the equation:
\[ 157 - 61 = 53i \]
\[ 96 = 53i \]
Next, we divide both sides by 53 to solve for \(i\):
\[ i = \frac{96}{53} \]
Therefore, \( i = \frac{96}{53} \).
### Answer: \( i = \frac{96}{53} \)
Expected answer: 96/53
Correct? Yes
Problem: Solve the following linear equation for the value of q: 71 = ((24 * q) + 14)
Gemma 2B:
To solve the equation 71 = 24q + 14 for q, we first isolate the term with q by subtracting 14 from both sides: 71 - 14 = 24q 57 = 24q Next, we divide both sides by 24 to solve for q: q = 57/24 q = 2.375 ### Answer: q = 2.375
Expected answer: 19/8
Correct? Yes
Problem: Solve the following linear equation for the value of i: 163 = 96 + 14 * i
Gemma 2B:
To solve for the value of \( i \), we first isolate the term with \( i \) on one side of the equation.
Given equation: \( 163 = 96 + 14i \)
Subtract 96 from both sides:
\( 163 - 96 = 96 - 96 + 14i \)
\( 67 = 14i \)
Divide by 14 on both sides to solve for \( i \):
\( i = \frac{67}{14} \)
Therefore, \( i = 4.7857 \) (rounded to four decimal places).
### Answer: \( i = 4.7857 \)
Expected answer: 67/14
Correct? No
Problem: Solve the following linear equation for the value of e: 59 = (70 * e) - 23
Gemma 2B:
To solve for the value of \( e \), we first isolate \( e \) by adding 23 to both sides of the equation:
\( 59 + 23 = 70e \)
\( 82 = 70e \)
Next, we divide both sides by 70 to solve for \( e \):
\( e = \frac{82}{70} \)
\( e = \frac{41}{35} \)
\( e = 1.17142857143 \)
### Answer: \( e = 1.17142857143 \)
Expected answer: 41/35
Correct? No
Problem: Solve the following linear equation for o: 147 = 36 * o + 74
Gemma 2B:
To solve for \( o \), we first isolate \( 36 \times o \) by subtracting 74 from both sides:
\( 147 - 74 = 36 \times o \)
\( 73 = 36 \times o \)
Next, we divide both sides by 36 to solve for \( o \):
\( o = \frac{73}{36} \)
\( o = 2.02777777778 \)
### Answer: \( o = 2.03 \)
Expected answer: 73/36
Correct? No
Problem: Solve the following equation: 71 = 93 - (13 * d)
Gemma 2B:
To solve the equation 71 = 93 - 13d, we first isolate the term involving d by subtracting 93 from both sides: 71 - 93 = 93 - 93 - 13d -22 = -13d Next, we solve for d by dividing both sides by -13: -22 / -13 = -13d / -13 d = 22/13 d = 1.6923 (rounded to four decimal places) ### Answer: d = 1.6923.
Expected answer: 22/13
Correct? No
Problem: Solve the following equation to find the value of n: 118 = 64 + 6 * n
Gemma 2B:
Reasoning: To solve for \( n \), we first subtract 64 from both sides of the equation:
\[ 118 - 64 = 6n \]
\[ 54 = 6n \]
Next, we divide both sides by 6 to solve for \( n \):
\[ n = \frac{54}{6} \]
\[ n = 9 \]
### Answer: \( n = 9 \)
Expected answer: 9
Correct? Yes
Problem: Solve the following equation to find the value of 'd': 61 = ((5 * d) - 7)
Gemma 2B:
To solve the equation, we first isolate the variable 'd' by undoing the operations in reverse order. 1. Add 7 to both sides: 61 + 7 = 5d 68 = 5d 2. Divide by 5: d = 68/5 d = 13.6 ### Answer: d = 13.6
Expected answer: 68/5
Correct? Yes
Problem: Solve the following linear equation for the value of z: 79 = ((8 * z) - 18)
Gemma 2B:
To solve the equation 79 = 8z - 18 for z, we first add 18 to both sides to isolate the term with z: 79 + 18 = 8z 97 = 8z Next, we divide both sides by 8 to solve for z: z = 97/8 z = 12.125 ### Answer: z = 12.125
Expected answer: 97/8
Correct? Yes
Problem: Solve the following linear equation for the value of z: 129 = ((2 * z) + 63)
Gemma 2B:
To solve the equation, we first need to isolate the variable z. Subtract 63 from both sides: 129 - 63 = 2z 66 = 2z Divide by 2 on both sides: 66/2 = z 33 = z ### Answer: z = 33
Expected answer: 33
Correct? Yes
Problem: Solve the following linear equation for e: 127 = (29 + (32 * e))
Gemma 2B:
To solve for \( e \), we first distribute the 32 on the right side of the equation:
\[ 127 = 29 + 32e \]
Next, we isolate the term with \( e \) by subtracting 29 from both sides:
\[ 127 - 29 = 32e \]
\[ 98 = 32e \]
Finally, we solve for \( e \) by dividing both sides by 32:
\[ e = \frac{98}{32} = 3.0625 \]
### Answer: \( e = 3.0625 \)
Expected answer: 49/16
Correct? Yes
Problem: Solve the following linear equation for the value of x: 30 = ((50 * x) - 35)
Gemma 2B:
To solve the equation 30 = 50x - 35 for x, we first add 35 to both sides to isolate the term with x: 30 + 35 = 50x - 35 + 35 65 = 50x Next, we divide both sides by 50 to solve for x: 65/50 = 50x/50 x = 1.3 ### Answer: x = 1.3
Expected answer: 13/10
Correct? Yes
Problem: Solve the following equation for x: 66 = 9 + 10 * x
Gemma 2B:
To solve the equation 66 = 9 + 10x for x, we first subtract 9 from both sides to isolate the term with x: 66 - 9 = 9 + 10x - 9, 57 = 10x. Next, we divide both sides by 10 to solve for x: 57/10 = 10x/10, 5.7 = x. ### Answer: x = 5.7.
Expected answer: 57/10
Correct? Yes
Problem: Solve the following algebraic equation for the unknown variable a: 103 = ((38 * a) + 51)
Gemma 2B:
To solve for \(a\), we first isolate the term with \(a\) by subtracting 51 from both sides:
\(103 - 51 = 38a\)
\(52 = 38a\)
Next, we divide both sides by 38 to solve for \(a\):
\(a = \frac{52}{38} = \frac{26}{19}\)
### Answer: \(a = \frac{26}{19}\)
Expected answer: 26/19
Correct? Yes
Problem: Determine the value of f in the following equation: 105 = 28 * f + 8
Gemma 2B:
To find the value of \( f \), we need to isolate \( f \) in the equation.
First, we subtract 8 from both sides of the equation:
\( 105 - 8 = 28f \)
\( 97 = 28f \)
Next, we divide both sides by 28 to solve for \( f \):
\( f = \frac{97}{28} \)
\( f = 3.46428571429 \) (rounded to 11 decimal places)
### Answer: \( f = 3.46428571429 \)
Expected answer: 97/28
Correct? No
Problem: Solve the linear equation for u: 12 = 63 - 50 * u
Gemma 2B:
To solve the linear equation for \( u \), we need to isolate \( u \) on one side of the equation.
Given equation: \( 12 = 63 - 50u \)
Subtract 63 from both sides:
\( 12 - 63 = -50u \)
Simplify:
\( -51 = -50u \)
Divide by -50:
\( u = \frac{-51}{-50} = \frac{51}{50} \)
### Answer: \( u = \frac{51}{50} \)
Expected answer: 51/50
Correct? Yes
Problem: Solve the following equation for the value of 'b': 60 = 42 + (10 * b)
Gemma 2B:
To solve for 'b', we first need to isolate 'b' on one side of the equation. Subtract 42 from both sides: 60 - 42 = 42 - 42 + 10b 18 = 10b Divide both sides by 10 to solve for 'b': 18/10 = 10b/10 1.8 = b ### Answer: b = 1.8
Expected answer: 9/5
Correct? Yes
Problem: Solve the following linear equation for the variable 'j': 84 = ((25 * j) + 13)
Gemma 2B:
To solve the equation 84 = 25j + 13 for j, we first isolate the term with j by subtracting 13 from both sides: 84 - 13 = 25j 71 = 25j Next, we divide both sides by 25 to solve for j: 71/25 = j j = 2.84 ### Answer: j = 2.84
Expected answer: 71/25
Correct? Yes
Problem: Solve the following linear equation for s: 153 = 91 + 5 * s
Gemma 2B:
To solve for \( s \), we first isolate \( s \) by subtracting 91 from both sides of the equation:
\[ 153 - 91 = 91 - 91 + 5s \]
\[ 62 = 5s \]
Next, we divide both sides by 5 to solve for \( s \):
\[ \frac{62}{5} = \frac{5s}{5} \]
\[ 12.4 = s \]
### Answer: \( s = 12.4 \)
Expected answer: 62/5
Correct? Yes
Problem: Solve for g in the following equation: 65 = (22 + (30 * g))
Gemma 2B:
Reasoning: First, we distribute the multiplication to get 65 = 22 + 30g. Then, we isolate the variable g by subtracting 22 from both sides to get 43 = 30g. Finally, we divide by 30 to solve for g, which gives us g = 43/30 = 1.43. ### Answer: g = 1.43
Expected answer: 43/30
Correct? No
Problem: Solve the following linear equation for the value of f: 96 = ((29 * f) + 10)
Gemma 2B:
To solve the equation 96 = 29f + 10 for f, we first isolate the term with f by subtracting 10 from both sides: 96 - 10 = 29f 86 = 29f Next, we divide both sides by 29 to solve for f: f = 86/29 f = 2.9655 (rounded to four decimal places) ### Answer: f = 2.9655.
Expected answer: 86/29
Correct? No
Problem: Solve the following equation for the variable q: 80 = (19 + (14 * q))
Gemma 2B:
First, distribute the 14 to q: 80 = 19 + 14q. Next, isolate the term with q by subtracting 19 from both sides: 80 - 19 = 14q. Simplify the left side: 61 = 14q. Finally, divide by 14 to solve for q: q = 61/14. ### Answer: q = 61/14.
Expected answer: 61/14
Correct? Yes
Problem: Solve the following linear equation for the variable 'm': 145 = 95 + 46 * m
Gemma 2B:
To solve the equation 145 = 95 + 46m for m, we first isolate the term with m by subtracting 95 from both sides: 145 - 95 = 95 - 95 + 46m 50 = 46m Next, we divide both sides by 46 to solve for m: m = 50/46 m = 25/23 ### Answer: m = 25/23.
Expected answer: 25/23
Correct? Yes
Problem: Solve the following equation for the value of 'i': 68 = 13 + 6 * i
Gemma 2B:
To solve for 'i', we first isolate the term with 'i' by subtracting 13 from both sides: 68 - 13 = 13 + 6i - 13, 55 = 6i. Next, we isolate 'i' by dividing both sides by 6: 55/6 = 6i/6, i = 55/6. Therefore, the value of 'i' is i = 55/6. ### Answer: i = 55/6.
Expected answer: 55/6
Correct? Yes
Problem: Solve the following equation for the value of h: 25 = ((74 * h) - 61)
Gemma 2B:
To solve for h, we first isolate the term with h by moving the constant term to the other side of the equation: 74h = 25 + 61 74h = 86 Next, we divide both sides by 74 to solve for h: h = 86/74 h = 43/37 ### Answer: h = 43/37.
Expected answer: 43/37
Correct? Yes
Problem: Solve the following linear equation for the value of q: 51 = ((6 * q) - 30)
Gemma 2B:
To solve the equation 51 = 6q - 30 for q, we first add 30 to both sides to isolate the term with q: 51 + 30 = 6q 81 = 6q Next, we divide both sides by 6 to solve for q: q = 81/6 q = 13.5 ### Answer: q = 13.5
Expected answer: 27/2
Correct? Yes
Problem: Find the value of r in the following linear equation: 38 = 81 - 36 * r
Gemma 2B:
Reasoning: To find the value of \( r \), we need to isolate \( r \) in the equation. First, we subtract 81 from both sides:
\( 38 = 81 - 36r \)
\( -43 = -36r \)
Next, we divide both sides by -36 to solve for \( r \):
\( r = \frac{-43}{-36} = \frac{43}{36} \)
### Answer: \( r = \frac{43}{36} \)
Expected answer: 43/36
Correct? Yes
Problem: Solve the following equation: 90 = (23 + (56 * a))
Gemma 2B:
To solve the equation 90 = 23 + 56a, we first isolate the term with the variable by subtracting 23 from both sides: 90 - 23 = 23 + 56a - 23, 67 = 56a. Next, we isolate the variable by dividing both sides by 56: 67/56 = (56a)/56, a = 67/56. Therefore, the solution to the equation is a = 67/56. ### Answer: a = 67/56.
Expected answer: 67/56
Correct? Yes
Problem: Solve the following linear equation for the unknown variable h: 81 = 13 + 30 * h
Gemma 2B:
To solve the equation 81 = 13 + 30h for h, we first isolate the term with h by subtracting 13 from both sides: 81 - 13 = 13 + 30h - 13, 68 = 30h. Next, we isolate h by dividing both sides by 30: h = 68/30, h = 2.27. ### Answer: h = 2.27.
Expected answer: 34/15
Correct? No
Problem: Solve the following linear equation for the value of m: 160 = ((62 * m) + 69)
Gemma 2B:
To solve for \( m \), we first distribute the 62 to \( m \) and then isolate \( m \) by subtracting 69 from both sides:
\[ 160 = 62m + 69 \]
\[ 160 - 69 = 62m \]
\[ 91 = 62m \]
\[ m = \frac{91}{62} \]
Therefore, \( m = \frac{91}{62} \).
### Answer: \( m = \frac{91}{62} \)
Expected answer: 91/62
Correct? Yes
Problem: Solve the following equation to find the value of q: 100 = 69 + 28 * q
Gemma 2B:
First, we need to isolate the variable q by subtracting 69 from both sides of the equation: 100 - 69 = 69 - 69 + 28q 31 = 28q Next, we divide both sides by 28 to solve for q: 31/28 = q ### Answer: q = 31/28.
Expected answer: 31/28
Correct? Yes
Problem: Solve the following linear equation to find the value of w: 192 = ((98 * w) + 94)
Gemma 2B:
First, we need to isolate the variable w by performing the necessary operations to solve for w. 192 = 98w + 94 Subtract 94 from both sides: 192 - 94 = 98w 98 = 98w Divide by 98 on both sides: w = 98/98 w = 1 ### Answer: w = 1
Expected answer: 1
Correct? Yes
Problem: Solve the following equation to find the value of y: 40 = 93 - 33 * y
Gemma 2B:
First, let's isolate the term with y by moving the constant term to the other side of the equation: 93 - 40 = 33y 53 = 33y Next, divide both sides by 33 to solve for y: y = 53/33 y = 1.606 ### Answer: y = 1.606
Expected answer: 53/33
Correct? No
Problem: Solve for the unknown variable u in the following linear equation: 74 = ((48 * u) - 20)
Gemma 2B:
First, we isolate the term with the variable u by adding 20 to both sides of the equation: 74 + 20 = 48u 94 = 48u Next, we divide both sides by 48 to solve for u: 94/48 = u u = 94/48 u = 47/24 ### Answer: u = 47/24.
Expected answer: 47/24
Correct? Yes
Problem: Solve the following equation for the variable f: 13 = ((86 * f) - 76)
Gemma 2B:
To solve for \( f \), we first isolate the term with \( f \) by moving the constant term to the other side of the equation:
\( 13 = 86f - 76 \)
Adding 76 to both sides:
\( 13 + 76 = 86f \)
\( 89 = 86f \)
Dividing by 86:
\( f = \frac{89}{86} \)
Therefore, \( f = \frac{89}{86} \).
### Answer: \( f = \frac{89}{86} \)
Expected answer: 89/86
Correct? Yes
Problem: Solve the following equation for c: 122 = (36 + (56 * c))
Gemma 2B:
To solve for c, we first simplify the equation: 122 = 36 + 56c Subtract 36 from both sides: 122 - 36 = 56c 86 = 56c Divide by 56 on both sides to solve for c: c = 86/56 = 43/28 ### Answer: c = 43/28.
Expected answer: 43/28
Correct? Yes
Problem: Solve the following linear equation for the unknown quantity q: 186 = 99 + 81 * q
Gemma 2B:
To solve the equation 186 = 99 + 81q for q, we first subtract 99 from both sides to isolate the term with q: 186 - 99 = 99 - 99 + 81q 87 = 81q Next, we divide both sides by 81 to solve for q: 87/81 = (81q)/81 q = 87/81 q = 1.074 ### Answer: q = 1.074
Expected answer: 29/27
Correct? No
Problem: Find the value of 'u' in the following equation: 120 = ((42 * u) + 77)
Gemma 2B:
Reasoning: To find the value of 'u', we first isolate the term with 'u' by subtracting 77 from both sides of the equation: 120 - 77 = 42u 43 = 42u Next, we divide both sides by 42 to solve for 'u': 43/42 = u u ≈ 1.0238 ### Answer: u ≈ 1.0238
Expected answer: 43/42
Correct? No
Problem: Solve the following equation to find the value of j: 103 = (52 + (6 * j))
Gemma 2B:
Reasoning: First, we distribute the 6 to j: 103 = 52 + 6j. Next, we isolate the term with j by subtracting 52 from both sides: 103 - 52 = 6j. Then, we simplify the left side: 51 = 6j. Finally, we solve for j by dividing both sides by 6: j = 51/6 = 8.5. ### Answer: j = 8.5.
Expected answer: 17/2
Correct? Yes
Problem: Solve the following linear equation for the value of n: 56 = (82 - (4 * n))
Gemma 2B:
To solve the equation 56 = (82 - 4n) for n, we first need to isolate the term with n on one side of the equation. Subtract 82 from both sides: 56 - 82 = -4n Simplify the left side: -26 = -4n Divide by -4 to solve for n: n = -26 / -4 n = 6.5 ### Answer: n = 6.5
Expected answer: 13/2
Correct? Yes
Problem: Solve the following linear equation for m: 77 = 14 + 60 * m
Gemma 2B:
To solve for \( m \), we first isolate \( m \) by subtracting 14 from both sides of the equation:
\[ 77 - 14 = 60m \]
\[ 63 = 60m \]
Next, we divide both sides by 60 to solve for \( m \):
\[ m = \frac{63}{60} = \frac{21}{20} \]
### Answer: \( m = \frac{21}{20} \)
Expected answer: 21/20
Correct? Yes
Problem: Solve the following linear equation for the variable 'e': 31 = 17 + e
Gemma 2B:
Reasoning: To solve for 'e', we need to isolate 'e' on one side of the equation. Subtract 17 from both sides: 31 - 17 = 17 + e - 17 14 = e ### Answer: e = 14
Expected answer: 14
Correct? Yes
Problem: Find the value of x that solves the following equation: 2 = 81 - (15 * x)
Gemma 2B:
Reasoning: To solve for x, we first isolate the term with x by moving the constant term to the other side of the equation. 2 = 81 - 15x 2 - 81 = -15x -79 = -15x Next, we solve for x by dividing both sides by -15. x = -79 / -15 x = 79/15 x = 5.27 (rounded to two decimal places) ### Answer: x = 5.27
Expected answer: 79/15
Correct? No
Problem: Solve the following equation for the value of e: 177 = 88 + 6 * e.
Gemma 2B:
To solve the equation 177 = 88 + 6 * e for the value of e, we first subtract 88 from both sides to isolate the term with e: 177 - 88 = 88 + 6e - 88, 89 = 6e. Next, we divide both sides by 6 to solve for e: e = 89 / 6, e = 14.83. ### Answer: e = 14.83.
Expected answer: 89/6
Correct? No
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 first isolate the variable 'r' by subtracting 15 from both sides: 95 - 15 = 3r 80 = 3r Next, we divide both sides by 3 to solve for 'r': 80/3 = r r = 80/3 r = 26.67 ### Answer: r = 26.67
Expected answer: 80/3
Correct? No
Problem: Solve the following linear equation for the value of v: 154 = (70 + (31 * v))
Gemma 2B:
First, distribute the 31 to v: 154 = 70 + 31v Subtract 70 from both sides: 154 - 70 = 31v 84 = 31v Divide by 31 to solve for v: v = 84/31 v = 2.7096774193548387 ### Answer: v = 2.71
Expected answer: 84/31
Correct? No
Problem: Solve the following equation for the value of r: 179 = ((70 * r) + 87)
Gemma 2B:
To solve for the value of \( r \), we first isolate the term with \( r \) by subtracting 87 from both sides:
\( 179 - 87 = 70r \)
\( 92 = 70r \)
Next, we divide both sides by 70 to solve for \( r \):
\( r = \frac{92}{70} \)
\( r = \frac{46}{35} \)
Therefore, the value of \( r \) is \( \frac{46}{35} \).
### Answer: \( r = \frac{46}{35} \)
Expected answer: 46/35
Correct? Yes
Problem: Solve the following equation to find the value of r: 93 = ((19 * r) + 2)
Gemma 2B:
To solve for \( r \), we first isolate the term with \( r \) by subtracting 2 from both sides:
\( 93 - 2 = 19r \)
\( 91 = 19r \)
Next, we divide both sides by 19 to solve for \( r \):
\( r = \frac{91}{19} \)
\( r = 4.789 \)
### Answer: \( r = 4.789 \)
Expected answer: 91/19
Correct? No
Problem: Solve the following linear equation for the value of z: 20 = (67 - (37 * z))
Gemma 2B:
First, let's simplify the equation: 20 = 67 - 37z Next, let's isolate the variable z by moving 67 to the other side of the equation: 20 + 37z = 67 37z = 47 Finally, divide by 37 to solve for z: z = 47/37 So, z = 47/37. ### Answer: z = 47/37.
Expected answer: 47/37
Correct? Yes
Problem: Solve the following linear equation for m: 65 = ((25 * m) + 15)
Gemma 2B:
Reasoning: First, distribute the 25 to m: 65 = 25m + 15. Next, isolate the term with m by subtracting 15 from both sides: 65 - 15 = 25m. Then, simplify the left side: 50 = 25m. Finally, divide by 25 to solve for m: m = 50/25 = 2. ### Answer: m = 2.
Expected answer: 2
Correct? Yes
Problem: Solve the following linear equation for g: 79 = ((6 * g) + 19)
Gemma 2B:
Reasoning: To solve for \( g \), we first isolate \( 6g \) by subtracting 19 from both sides:
\[ 79 = 6g + 19 \]
\[ 60 = 6g \]
Then, we divide both sides by 6 to solve for \( g \):
\[ g = \frac{60}{6} \]
\[ g = 10 \]
### Answer: \( g = 10 \)
Expected answer: 10
Correct? Yes
Problem: Solve the following linear equation for the variable 'l': 30 = ((56 * l) - 45)
Gemma 2B:
To solve the equation 30 = 56l - 45 for the variable 'l', we first add 45 to both sides to isolate the term with 'l': 30 + 45 = 56l - 45 + 45, 75 = 56l. Next, we divide both sides by 56 to solve for 'l': 75/56 = (56l)/56, l = 75/56. Therefore, the solution to the equation is l = 75/56. ### Answer: l = 75/56.
Expected answer: 75/56
Correct? Yes
Problem: Solve the following equation to find the value of j: 57 = ((11 * j) + 4)
Gemma 2B:
First, we isolate the variable j by subtracting 4 from both sides of the equation: 57 - 4 = 11j 53 = 11j Then, we divide both sides by 11 to solve for j: 53/11 = j j = 4.818181... ### Answer: j = 4.818181...
Expected answer: 53/11
Correct? No
Problem: Solve the following equation to find the value of 'f': 36 = 34 * f - 56
Gemma 2B:
To solve for 'f', we first isolate 'f' by adding 56 to both sides of the equation: 34 * f = 36 + 56 34 * f = 92 Then, we divide both sides by 34 to solve for 'f': f = 92/34 f = 2.70588235294 (rounded to 2 decimal places) ### Answer: f = 2.71
Expected answer: 46/17
Correct? No
Problem: Solve the following linear equation to find the value of 'u': 56 = (70 * u) - 43
Gemma 2B:
To solve the equation, we first isolate the variable 'u' by adding 43 to both sides: 56 + 43 = 70u 99 = 70u Next, we divide both sides by 70 to solve for 'u': u = 99/70 u = 1.41 ### Answer: u = 1.41
Expected answer: 99/70
Correct? No
Problem: Solve the following equation for the variable x: 67 = 21 + 9*x
Gemma 2B:
To solve for x, we first isolate the term with x by subtracting 21 from both sides: 67 - 21 = 21 + 9x - 21, 46 = 9x. Next, we divide both sides by 9 to solve for x: 46/9 = 9x/9, 5.11 = x. ### Answer: x = 5.11.
Expected answer: 46/9
Correct? No
Problem: Determine the unknown variable in the following equation: 75 = (58 + 16 * i)
Gemma 2B:
Reasoning: To solve for \( i \), we first simplify the expression on the right side of the equation: \( 58 + 16i = 75 \) \( 16i = 75 - 58 \) \( 16i = 17 \) \( i = 17/16 \) ### Answer: \( i = 17/16 \)
Expected answer: 17/16
Correct? Yes
Problem: Solve for x in the following equation: 111 = (54 + (39 * x))
Gemma 2B:
Reasoning: To solve for x, we first simplify the expression on the right side of the equation.
\(54 + (39 \times x) = 54 + 39x\).
Now, we substitute this back into the equation: \(111 = 54 + 39x\).
Subtracting 54 from both sides gives us: \(111 - 54 = 39x\).
\(57 = 39x\).
Dividing both sides by 39 gives us: \(x = \frac{57}{39} = \frac{19}{13}\).
### Answer: \(x = \frac{19}{13}\)
Expected answer: 19/13
Correct? Yes
Problem: Solve the following equation to find the value of 'o': 155 = ((26 * o) + 68)
Gemma 2B:
Reasoning: To solve for 'o', we first isolate 'o' by subtracting 68 from both sides of the equation: 155 - 68 = 26 * o 87 = 26 * o Next, we divide both sides by 26 to solve for 'o': 87/26 = o o = 3.34615384615 ### Answer: o = 3.35
Expected answer: 87/26
Correct? No
Problem: Solve for p in the following equation: 7 = ((12 * p) - 17)
Gemma 2B:
To solve for \( p \), we first isolate \( p \) by moving the constant term to the other side of the equation and then dividing by the coefficient of \( p \).
\( 7 = 12p - 17 \)
Adding 17 to both sides:
\( 7 + 17 = 12p \)
\( 24 = 12p \)
Dividing by 12:
\( p = \frac{24}{12} \)
\( p = 2 \)
### Answer: \( p = 2 \)
Expected answer: 2
Correct? Yes
Problem: Solve the following problem: What is the value of the variable 'b' if 163 = 93 + 55 * b?
Gemma 2B:
Reasoning: First, we need to isolate the variable 'b' by subtracting 93 from both sides of the equation: 163 - 93 = 93 + 55b - 93, 70 = 55b. Next, we divide both sides by 55 to solve for 'b': 70/55 = 55b/55, b = 70/55, b = 14/11. ### Answer: b = 14/11.
Expected answer: 14/11
Correct? Yes
Problem: Solve the linear equation for the value of 'u': 62 = (u - 26)
Gemma 2B:
To solve for 'u', we need to isolate 'u' on one side of the equation. Adding 26 to both sides of the equation, we get: 62 + 26 = u - 26 + 26 88 = u Therefore, the value of 'u' is 88. ### Answer: u = 88
Expected answer: 88
Correct? Yes
Problem: Solve the following equation for the variable a: 179 = ((63 * a) + 93)
Gemma 2B:
To solve for \(a\), we first isolate the term with \(a\) by subtracting 93 from both sides:
\(179 - 93 = 63a\)
\(86 = 63a\)
Next, we divide both sides by 63 to solve for \(a\):
\(a = \frac{86}{63}\)
Therefore, \(a = \frac{86}{63}\).
### Answer: \(a = \frac{86}{63}\)
Expected answer: 86/63
Correct? Yes
Problem: Find the value of c in the equation: 51 = ((27 * c) - 11)
Gemma 2B:
To find the value of \( c \), we first isolate \( c \) by adding 11 to both sides of the equation:
\( 51 + 11 = 27c \)
\( 62 = 27c \)
Next, we divide both sides by 27 to solve for \( c \):
\( c = \frac{62}{27} \)
\( c = 2 \frac{8}{27} \)
### Answer: \( c = 2 \frac{8}{27} \)
Expected answer: 62/27
Correct? Yes
Problem: Solve the following equation for 'd': 19 = ((28 * d) - 18)
Gemma 2B:
To solve the equation 19 = 28d - 18 for 'd', we first add 18 to both sides to isolate the term with 'd': 19 + 18 = 28d - 18 + 18 37 = 28d Next, we divide both sides by 28 to solve for 'd': 37/28 = 28d/28 d = 37/28 Therefore, the solution to the equation is d = 37/28. ### Answer: d = 37/28.
Expected answer: 37/28
Correct? Yes
Problem: Solve the following linear equation for the value of e: 159 = ((47 * e) + 62)
Gemma 2B:
First, we need to isolate the variable e by performing the following steps: 159 = 47e + 62 Subtract 62 from both sides: 159 - 62 = 47e 97 = 47e Divide by 47 on both sides to solve for e: e = 97/47 e = 2.06 (rounded to two decimal places) ### Answer: e = 2.06
Expected answer: 97/47
Correct? No
Problem: Solve the following linear equation for the variable g: 145 = (50 + (91 * g))
Gemma 2B:
To solve for \( g \), we first distribute the multiplication:
\[ 145 = 50 + 91g \]
Next, we isolate the term with \( g \) by subtracting 50 from both sides:
\[ 145 - 50 = 91g \]
\[ 95 = 91g \]
Finally, we solve for \( g \) by dividing both sides by 91:
\[ g = \frac{95}{91} = 1.\overline{04} \]
### Answer: \( g = \frac{95}{91} \)
Expected answer: 95/91
Correct? Yes
Problem: Solve the following linear equation for the value of l: 123 = ((44 * l) + 73)
Gemma 2B:
To solve the equation 123 = 44l + 73 for the value of l, we first isolate the term with l by subtracting 73 from both sides: 123 - 73 = 44l 50 = 44l Next, we divide both sides by 44 to solve for l: l = 50/44 l = 25/22 ### Answer: l = 25/22.
Expected answer: 25/22
Correct? Yes
Problem: Solve the following equation: 165 = ((19 * q) + 75)
Gemma 2B:
To solve the equation 165 = 19q + 75, we first isolate the variable q by subtracting 75 from both sides: 165 - 75 = 19q 90 = 19q Next, we divide both sides by 19 to solve for q: q = 90/19 q = 4.73684210526 (approximately) ### Answer: q = 4.73684210526 (approximately)
Expected answer: 90/19
Correct? No
Problem: Solve the following linear equation to find the value of g: 149 = ((18 * g) + 62)
Gemma 2B:
To solve the equation 149 = 18g + 62, we first isolate the term with g by subtracting 62 from both sides: 149 - 62 = 18g 87 = 18g Next, we divide both sides by 18 to solve for g: g = 87/18 g = 4.8333 (rounded to four decimal places) ### Answer: g = 4.8333.
Expected answer: 29/6
Correct? No
Problem: Solve the following linear equation for the variable d: 84 = 20 * d + 21
Gemma 2B:
To solve for \(d\), we need to isolate \(d\) on one side of the equation.
First, we subtract 21 from both sides of the equation:
\[ 84 - 21 = 20d \]
\[ 63 = 20d \]
Next, we divide both sides by 20 to solve for \(d\):
\[ d = \frac{63}{20} \]
\[ d = 3.15 \]
### Answer: \( d = 3.15 \)
Expected answer: 63/20
Correct? Yes
Problem: Solve the following equation to find the value of g: 61 = (50 + (6 * g))
Gemma 2B:
To solve for \( g \), we first distribute the 6 on the right side of the equation:
\[ 61 = 50 + 6g \]
Next, we isolate the term with \( g \) by subtracting 50 from both sides:
\[ 61 - 50 = 6g \]
\[ 11 = 6g \]
Finally, we solve for \( g \) by dividing both sides by 6:
\[ g = \frac{11}{6} \]
So, \( g = \frac{11}{6} \).
### Answer: \( g = \frac{11}{6} \)
Expected answer: 11/6
Correct? Yes
Problem: Solve the following linear equation for the unknown variable v: 126 = ((21 * v) + 76)
Gemma 2B:
To solve for \( v \), we first isolate the term with \( v \) by subtracting 76 from both sides:
\( 126 - 76 = 21v \)
\( 50 = 21v \)
Next, we divide both sides by 21 to solve for \( v \):
\( v = \frac{50}{21} \)
Therefore, \( v = \frac{50}{21} \) or approximately \( v \approx 2.38 \).
### Answer: \( v = \frac{50}{21} \)
Expected answer: 50/21
Correct? Yes
Problem: Solve the following linear equation for g: 74 = ((91 * g) - 24)
Gemma 2B:
To solve the equation 74 = 91g - 24 for g, we first add 24 to both sides to isolate the term with g: 74 + 24 = 91g - 24 + 24, 98 = 91g. Next, we divide both sides by 91 to solve for g: 98/91 = (91g)/91, g = 98/91. Therefore, the solution to the equation is g = 98/91. ### Answer: g = 98/91.
Expected answer: 14/13
Correct? Yes