Question:
The set $\{5, 8, 10, 18, 19, 28, 30, x\}$ has eight members. The mean of the set's members is 4.5 less than $x$. What is the value of $x$ ?

Answer:
Setting the mean of the set's members equal to $x - 4.5$, we get the equation \[\frac{5+8+10+18+19+28+30+x}{8}=x-4.5.\]Simplifying the left-hand side, we get \[\frac{118+x}{8} = x - 4.5.\]Multiplying by $8$ gives $118+x = 8x-36$. Then $7x = 118+36=154$. Thus $x=\frac{154}{7} = \boxed{22}.$