Answer
$x=\left\{ -13,7 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x+3|=12-2
,$ 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+3|=10
.\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+3=10
\\\\\text{OR}\\\\
x+3=-10
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+3=10
\\\\
x=10-3
\\\\
x=7
\\\\\text{OR}\\\\
x+3=-10
\\\\
x=-10-3
\\\\
x=-13
.\end{array}
Hence, $
x=\left\{ -13,7 \right\}
.$