Answer
$x\leq-7$
$x\geq-3$
OR
$(-\infty, -7)$ and $(-3, \infty)$
Work Step by Step
Given
$|x+5|\geq2$
By absolute value definition
$x+5\leq-2$ or $x+5\geq2$
Subtract 5
ANSWER
$x\leq-7$
$x\geq-3$
OR
$(-\infty, -7)$ and $(-3, \infty)$