Answer
$x=-\dfrac{1}{5}$
Work Step by Step
The given inequality, $
|5x+1|\le0
,$ is equivalent to
\begin{array}{l}\require{cancel}
5x+1=0
.\end{array}
Using the properties of equality, the solution to the equation above is
\begin{array}{l}\require{cancel}
5x=-1
\\\\
x=-\dfrac{1}{5}
.\end{array}