Answer
$x=-\dfrac{6}{5}$
Work Step by Step
The left side of the given expression, $
\left| \dfrac{5x+6}{2} \right|\le0
,$ always gives a non-negative value. Hence, the solution set to the given inequality is
\begin{array}{l}\require{cancel}
\dfrac{5x+6}{2}=0
\\\\
5x+6=0(2)
\\\\
5x+6=0
\\\\
5x=-6
\\\\
x=-\dfrac{6}{5}
.\end{array}