5. [6] What is the sum of all integers $x$ such that $|x+2| \leq 10$ ?
Answer: -42 The inequality $|x+2| \leq 10$ holds if and only if $x+2 \leq 10$ and $x+2 \geq-10$. So $x$ must be in the range $-12 \leq x \leq 8$. If we add up the integers in this range, each positive integer cancels with its additive inverse, so the sum is equal to $-12-11-10-9=-42$.