Answer
$x=\left\{ -75,175 \right\}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|0.02x-1|=2.50
,$ is equivalent to
\begin{array}{l}\require{cancel}
0.02x-1=2.50 \text{ OR } 0.02x-1=-2.50
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
0.02x-1=2.50
\\\\
100(0.02x-1)=(2.50)100
\\\\
2x-100=250
\\\\
2x=250+100
\\\\
2x=350
\\\\
x=\dfrac{350}{2}
\\\\
x=175
\\\\\text{ OR }\\\\
0.02x-1=-2.50
\\\\
100\left(0.02x-1\right)=(-2.50)100
\\\\
2x-100=-250
\\\\
2x=-250+100
\\\\
2x=-150
\\\\
x=-\dfrac{150}{2}
\\\\
x=-75
.\end{array}
Hence, the solutions are $
x=\left\{ -75,175 \right\}
.$