#### Answer

$ 0\leq z\leq 10,\qquad$ or, $ z\in [0,10]$

#### Work Step by Step

Use properties from the table 'Absolute Values and Intervals".
Applying Property 8:
$|x|\leq a\quad\Leftrightarrow\quad -a\leq x\leq a, \quad $ for a = positive number
We have:
$-1\displaystyle \leq\frac{z}{5}-1\leq 1\qquad $
Applying rule 1 for inequalities, add 1 to each part of the compound inequality.
$0\displaystyle \leq\frac{z}{5}\leq 2\qquad $
Apply rule 3: multiply with a positive number
$0\leq z\leq 10$
This is a closed interval, $[0,10]$
(see table: "Types of intervals".)