Answer
$x=\left\{ -14,10 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x+2|+6=18
,$ isolate first the absolute value expression. Then use the definition of absolute value equality. Do checking of the solution/s.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
|x+2|+6=18
\\\\
|x+2|=18-6
\\\\
|x+2|=12
.\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=12
\\\\\text{OR}\\\\
x+2=-12
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+2=12
\\\\
x=12-2
\\\\
x=10
\\\\\text{OR}\\\\
x+2=-12
\\\\
x=-12-2
\\\\
x=-14
.\end{array}
If $x=10,$ then
\begin{array}{l}\require{cancel}
|x+2|+6=18?
\\\\
|10+2|+6=18?
\\\\
|12|+6=18?
\\\\
12+6=18?
\\\\
18=18
\text{ (TRUE)}
.\end{array}
If $x=-14,$ then
\begin{array}{l}\require{cancel}
|x+2|+6=18?
\\\\
|-14+2|+6=18?
\\\\
|-12|+6=18?
\\\\
12+6=18?
\\\\
18=18
\text{ (TRUE)}
.\end{array}
Hence, $
x=\left\{ -14,10 \right\}
.$
