Answer
$x=-1$
Work Step by Step
Multiplying both sides by the $LCD=6$, then the solution to the given expression, $
\dfrac{1}{2}x+\dfrac{1}{3}=\dfrac{1}{6}x
$, is
\begin{array}{l}\require{cancel}
3(1x)+2(1)=1(1x)
\\\\
3x+2=x
\\\\
3x-x=-2
\\\\
2x=-2
\\\\
x=-\dfrac{2}{2}
\\\\
x=-1
.\end{array}