Answer
$x= \frac{25}{7}$
Work Step by Step
$\frac{3x}{5}-\frac{x-3}{2} = \frac{x+2}{3}$
Take LCD at the left hand side of the expression
$\frac{6x-5(x-3)}{10} = \frac{x+2}{3}$
$\frac{6x-5x+15}{10} = \frac{x+2}{3}$
$\frac{x+15}{10} = \frac{x+2}{3}$
Multiply both sides by 30 to clear fractional part.
$30(\frac{x+15}{10}) = 30(\frac{x+2}{3})$
$3(x+15) = 10(x+2)$
$3x+45 = 10x+20$
$45-20 = 10x-3x$
$25 = 7x$
$7x = 25$
$x= \frac{25}{7}$
