Answer
$[0,8]$
Work Step by Step
$|2-\displaystyle \frac{x}{2}|-1\leq 1 \qquad $... $/+1$
$|2-\displaystyle \frac{x}{2}|\leq 2 \qquad $... $/\times 2$
$|4-x|\leq 4 \qquad $... apply $|a-b|=|b-a|$
$|x-4|\leq 4$
... $|u| \leq c $ is equivalent to $\quad -c \leq u \leq c.$
$-4 \leq x-4 \leq 4 \qquad $... $/+4$
$ 0 \leq x \leq 8$
Borders are included it the interval.
Solution set: $[0,8]$
