#### Answer

$x=-\dfrac{2}{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $ |3x+2|\le0 ,$ use the properties of equality to solve for the equation $3x+2=0.$
$\bf{\text{Solution Details:}}$
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} 3x+2=0 .\end{array}
Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 3x=-2 \\\\ \dfrac{3x}{3}=-\dfrac{2}{3} \\\\
x=-\dfrac{2}{3}
.\end{array}