## Intermediate Algebra (6th Edition)

$[-2,18]$
We are given that $|-x+8|-2\leq8$. Add 2 to both sides. $|-x+8|\leq10$ Therefore, $-x+8\leq10$ and $-x+8\geq-10$. We can solve both equations to find solutions. For $-x+8\leq10$, subtract 8 from both sides. $-x\leq2$ Divide both sides by -1 (which will reverse the inequality sign). $x\geq-2$ For $-x+8\geq-10$, subtract 8 from both sides. $-x\geq-18$ Divide both sides by -1 (which will reverse the inequality sign). $x\leq18$ Therefore, the solution set consists of all values of x that are greater than or equal to -2 and less than or equal to 18.