Answer
$x=\left\{ \dfrac{11}{3},1 \right\}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given equation, $
|3x-7|=4
,$ is equivalent to
\begin{array}{l}\require{cancel}
3x-7=4 \text{ OR } 3x-7=-4
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x-7=4
\\\\
3x=4+7
\\\\
3x=11
\\\\
x=\dfrac{11}{3}
\\\\\text{ OR }\\\\
3x-7=-4
\\\\
3x=-4+7
\\\\
3x=3
\\\\
x=\dfrac{3}{3}
\\\\
x=1
.\end{array}
Hence, the solutions are $
x=\left\{ \dfrac{11}{3},1 \right\}
.$