#### Answer

$x=\left\{ -5,1 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x+2|=5-2
,$ simplify first the right side. Then use the definition of absolute value equality. Use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Simplifying the right side, the given equation is equivalent to
\begin{array}{l}\require{cancel}
|x+2|=3
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x+2=3
\\\\\text{OR}\\\\
x+2=-3
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+2=3
\\\\
x=3-2
\\\\
x=1
\\\\\text{OR}\\\\
x+2=-3
\\\\
x=-3-2
\\\\
x=-5
.\end{array}
Hence, $
x=\left\{ -5,1 \right\}
.$