Answer
$x=\left\{ -74,224 \right\}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|0.04x-3|=5.96
,$ is equivalent to
\begin{array}{l}\require{cancel}
0.04x-3=5.96 \text{ OR } 0.04x-3=-5.96
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
0.04x-3=5.96
\\\\
100(0.04x-3)=(5.96)100
\\\\
4x-300=596
\\\\
4x=596+300
\\\\
4x=896
\\\\
x=\dfrac{896}{4}
\\\\
x=224
\\\\\text{ OR }\\\\
0.04x-3=-5.96
\\\\
100(0.04x-3)=(-5.96)100
\\\\
4x-300=-596
\\\\
4x=-596+300
\\\\
4x=-296
\\\\
x=-\dfrac{296}{4}
\\\\
x=-74
.\end{array}
Hence, the solutions are $
x=\left\{ -74,224 \right\}
.$
