Answer
$-7\leq x\leq1$
Work Step by Step
The absolute value of multiple values can turn the right side positive or negative when broken down. With inequalities, it also flips the sign when the other side turns negative.
$|x+3|\leq4$
$x+3\leq4$
$x\leq1$
$x+3\geq-4$
$x\geq-7$
$-7\leq x\leq1$