Answer
$x=\dfrac{3}{8}$
Work Step by Step
The left side of the given expression, $
\left| \dfrac{8x-3}{4} \right|\le0
,$ always gives a non-negative value. Hence, the solution set to the given inequality is
\begin{array}{l}\require{cancel}
\dfrac{8x-3}{4}=0
\\\\
8x-3=0(4)
\\\\
8x-3=0
\\\\
8x=3
\\\\
x=\dfrac{3}{8}
.\end{array}