# Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 138: 92

$[0,8]$

#### 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: $[0,8]$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.