#### Answer

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

#### Work Step by Step

$1\leq|x|\leq 4$
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 $]$