Answer
$|x+2|\lt3$
Work Step by Step
Adding $2$ to all sides of the given inequality $
-5\lt x \lt 1
,$ then the given is equivalent to
\begin{array}{l}\require{cancel}
-5+2\lt x+2 \lt 1+2
\\\\
-3\lt x+2 \lt 3
.\end{array}
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to $
|x+2|\lt3
.$
