In the equation $|x-7| -3 = -2$, what is the product of all possible values of $x$?
We rearrange the given equation to $|x-7| = 1$.  Thus either $x-7 = 1$, meaning $x = 8$, or $x-7 = -1$, meaning $x=6$.  Our answer is therefore $6\cdot 8 = \boxed{48}$.
48
Level 3
Algebra
Problem: In the equation $|x-7| -3 = -2$, what is the product of all possible values of $x$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the equation |x-7| - 3 = -2, first isolate the absolute value term. Add 3 to both sides to obtain |x-7| = 1. The absolute value equation |x-7| = 1 implies two cases: x - 7 = 1 and x - 7 = -1. 

For the first case, x - 7 = 1, add 7 to both sides to find x = 8. For the second case, x - 7 = -1, add 7 to both sides to find x = 6. Thus, the possible values of x are 8 and 6. 

Next, calculate the product of these values. Multiply 8 by 6 to get 48. Therefore, the final answer is 48.<|END_OF_LATENT|> The final answer is $48$.