Answer
$\text{the interval }
\left( 2,\infty \right)
$
Work Step by Step
Using the properties of inequality, the solution to the given inequality, $
\dfrac{3(x-2)}{5}\gt\dfrac{-5(x-2)}{3}
,$ is
\begin{array}{l}\require{cancel}
15\cdot\dfrac{3(x-2)}{5}\gt\dfrac{-5(x-2)}{3}\cdot 15
\\\\
3\cdot3(x-2) \gt -5(x-2)\cdot 5
\\\\
9x-18 \gt -25x+50
\\\\
34x \gt 68
\\\\
x \gt \dfrac{68}{34}
\\\\
x \gt 2
.\end{array}
In interval notation, the solution is $
\text{the interval }
\left( 2,\infty \right)
.$
