Chapter 1, Equations and Graphs - Section 1.8 - Solving Absolute Value Equations and Inequalities - 1.8 Exercises - Page 153: 45

Interval: $[-4,\ -1]\cup [1$, 4 $]$

$1\leq|x|\leq 4$ There are two possibilities. If $x$ is positive, then $|x|=x$: $1\leq|x|\leq 4$ $1\leq x\leq 4$ If $x$ is negative, then $|x|=-x$: $1\leq|x|\leq 4$ $1\leq-x\leq 4$ $-1\geq x\geq-4 $ $-4\leq x\leq-1$ Interval: $[-4,\ -1]\cup [1$, 4 $]$