## Thomas' Calculus 13th Edition

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