#### Answer

$x=-\dfrac{1}{2} $

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $ |2x+1|\le0 ,$ use the properties of equality to solve for the equation $2x+1=0.$
$\bf{\text{Solution Details:}}$
The absolute value of $x$, written as $|x|,$ is the distance of $x$ to $0,$ and hence, is always a nonnegative number. The only time that the given expression will be satisfied is when \begin{array}{l}\require{cancel} 2x+1=0 .\end{array}
Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 2x=-1 \\\\ \dfrac{2x}{2}=-\dfrac{1}{2} \\\\ x=-\dfrac{1}{2} .\end{array}