Answer
Solution set = $\displaystyle \{\frac{25}{7}\}$
Work Step by Step
Multiply both sides with the LCD, $30$
$ 30 \left[\displaystyle \frac{3x}{5}-\frac{x-3}{2}\right]=30 \left[ \dfrac{x+2}{3} \right]\quad$ ... distribute and simplify
$ 6(3x)+15(x-3)=10(x+2)\quad$ ... distribute and simplify
$18x-15x+45=10x+20$
$ 3x+45=10x+20\quad$ ... add $-10x-45$ to both sides
$3x-10x=20-45$
$-7x=-25$
$x=\displaystyle \frac{-25}{-7}=\frac{25}{7}$
Solution set = $\displaystyle \{\frac{25}{7}\}$
