#### Answer

$(-11,7)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|x+2|\lt9
,$ use the definition of the absolute value less than a constant.
$\bf{\text{Solution Details:}}$
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
\begin{array}{l}\require{cancel}
-9\lt x+2\lt9
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-9-2\lt x+2-2\lt9-2
\\\\
-11\lt x\lt7
.\end{array}
Hence, the solution set is the interval $
(-11,7)
.$