Answer
$x=3$
Work Step by Step
Multiplying both sides by the $LCD=
2(5x-9)
$, the value of the variable that satisfies the given equation, $
\dfrac{2x+3}{5x-9}=\dfrac{3}{2}
,$ is
\begin{array}{l}\require{cancel}
2(2x+3)=(5x-9)(3)
\\\\
4x+6=15x-27
\\\\
4x-15x=-27-6
\\\\
-11x=-33
\\\\
x=\dfrac{-33}{-11}
\\\\
x=3
.\end{array}