Answer
$\left\{-6, 4\right\}$
Work Step by Step
RECALL:
$|x|=a \longrightarrow x=a \text{ or } x = -a$
Use the rule above to obtain:
$x+1 = 5 \text{ or } x+1 = -5$
Solve each equation to obtain:
$x = 5-1 \text{ or } x = -5 -1
\\x = 4 \text{ or } x =-6$
Thus, the solution set is $\left\{-6, 4\right\}$.
