#### Answer

$z=\left\{ -3,3 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
5|z|+2=17
,$ isolate first the absolute value expression. Then use the definition of an absolute value equality.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
5|z|+2=17
\\\\
5|z|=17-2
\\\\
5|z|=15
\\\\
|z|=\dfrac{15}{5}
\\\\
|z|=3
.\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}
z=3
\\\\\text{OR}\\\\
z=-3
.\end{array}
Hence, $
z=\left\{ -3,3 \right\}
.$