Answer
$x=\dfrac{1}{6}$
Work Step by Step
Using the properties of equality, the given equation, $
\dfrac{3}{2x}-\dfrac{2}{3x}=5
,$ is equivalent to
\begin{align*}\require{cancel}
6x\left( \dfrac{3}{2x}-\dfrac{2}{3x} \right)&=(5)6x
&\text{(multiply by the $LCD$)}
\\\\
3(3)-2(2)&=30x
\\
9-4&=30x
\\
5&=30x
\\\\
\dfrac{5}{30}&=\dfrac{30x}{30}
\\\\
\dfrac{1}{6}&=x
.\end{align*}
Hence, the solution is $
x=\dfrac{1}{6}
.$
