#### Answer

Interval: $(-\infty,\ -3]\ \cup\ [-1,\ \infty)$

#### Work Step by Step

$3-|2x+4|\leq 1$
$-|2x+4|\leq 1-3$
$-|2x+4|\leq-2$
$|2x+4|\geq 2$
We split the absolute value into the positive and negative:
$2x+4\geq 2$
$ 2x\geq-2$
$ x\geq-1$
$2x+4\leq-2$
$ 2x\leq-6$
$ x\leq-3$
Interval: $(-\infty,\ -3]\ \cup\ [-1,\ \infty)$