#### Answer

$\left\{ x| x=24 \right\}$

#### Work Step by Step

Multiplying both sides by the $LCD=
12
$, the given equation, $
\dfrac{x}{4}-\dfrac{2x}{3}=-10
,$ is equivalent to
\begin{array}{l}\require{cancel}
3(x)-4(2x)=12(-10)
\\\\
3x-8x=-120
\\\\
-5x=-120
\\\\
x=\dfrac{-120}{-5}
\\\\
x=24
.\end{array}
Hence, the solution is $
\left\{ x| x=24 \right\}
.$