Answer
$[-6,4]$
Work Step by Step
We are asked to solve the absolute value inequality:
$|x+1|\le 5$
We remove the absolute value sign by splitting the inequality into two as follows:
$-5 \le x+1 \le 5$
Now, we solve for (isolate) $x$:
$-5-1 \le x+1-1 \le 5-1$
$-6 \le x \le 4$
In interval notation, this can be written as:
$[-6,4]$
See the number line graph below.
