#### Answer

$x=\left\{ -\dfrac{1}{3}, 5 \right\}$

#### Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given equation, $
|3x-7|=8
,$ is equivalent to
\begin{array}{l}\require{cancel}
3x-7=8 \text{ OR } 3x-7=-8
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x-7=8
\\\\
3x=8+7
\\\\
3x=15
\\\\
x=\dfrac{15}{3}
\\\\
x=5
\\\\\text{ OR }\\\\
3x-7=-8
\\\\
3x=-8+7
\\\\
3x=-1
\\\\
x=-\dfrac{1}{3}
.\end{array}
Hence, the solutions are $
x=\left\{ -\dfrac{1}{3}, 5 \right\}
.$