#### Answer

$x=-\dfrac{1}{4}$

#### Work Step by Step

The given inequality, $
|4x+1|=0
,$ is equivalent to
\begin{array}{l}\require{cancel}
4x+1=0
.\end{array}
Using the properties of equality, the solution to the equation above is
\begin{array}{l}\require{cancel}
4x=-1
\\\\
x=-\dfrac{1}{4}
.\end{array}