Answer
$[-3,-1]$
Work Step by Step
We are asked to solve the absolute value inequality:
$|x+2|\le 1$
We remove the absolute value sign by splitting the inequality into two as follows:
$-1 \le x+2 \le 1$
Now, we solve for (isolate) $x$:
$-1-2 \le x+2-2 \le 1-2$
$-3 \le x \le -1$
In interval notation, this can be written as:
$[-3,-1]$
See the number line graph below.
