#### Answer

$x=\dfrac{35}{18}$

#### Work Step by Step

Multiplying both sides by the $LCD=
30
$ and using the properties of equality, the value of the variable that satisfies the given equation, $
\dfrac{3}{5}x-\dfrac{2}{3}=\dfrac{1}{2}
,$ is
\begin{array}{l}\require{cancel}
6(3x)-10(2)=15(1)
\\\\
18x-20=15
\\\\
18x=15+20
\\\\
18x=35
\\\\
x=\dfrac{35}{18}
.\end{array}