## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$|x+2|\lt3$
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 $|x+2|\lt3 .$