Answer
$[-2,18]$
Work Step by Step
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.
