#### Answer

$x=\left\{ -11,11 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Given that $
f(x)=|x|+7
,$ to find $x$ for which $
f(x)=18
,$ use substitution. Then isolate the absolute value expression and use the definition of an absolute value equality.
$\bf{\text{Solution Details:}}$
Replacing $f(x)$ with $
18
,$ then
\begin{array}{l}\require{cancel}
f(x)=|x|+7
\\\\
18=|x|+7
\\\\
|x|+7=18
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
|x|+7=18
\\\\
|x|=18-7
\\\\
|x|=11
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
x=11
\\\\\text{OR}\\\\
x=-11
.\end{array}
Hence, $
x=\left\{ -11,11 \right\}
.$