Answer
$x=-1$
Work Step by Step
The left side of the given equation $
\left| \dfrac{2(x+1)}{3} \right|\le0
,$ always results to a non negative number. This equation will only be satisfied when the left-side expression is equal to $0$. Hence, the solution to the given equation is
\begin{array}{l}\require{cancel}
\dfrac{2(x+1)}{3}=0
\\\\
2(x+1)=3(0)
\\\\
2x+2=0
\\\\
2x=-2
\\\\
x=-\dfrac{2}{2}
\\\\
x=-1
.\end{array}
