$\dfrac{-(x - 3)}{2} - 2 = \dfrac{(5(x+2)}{4}$
$⇒ \dfrac{-(x - 3)}{2} - 2 = \dfrac{5x + 10}{4}$
$⇒ \dfrac{-(x - 3)}{2} - \dfrac{4}{2} = \dfrac{5x + 10}{4}$
$⇒ \dfrac{-(x - 3)2 - 8}{4} = \dfrac{5x + 10}{4}$
$⇒ -2(x-3)-8 = 5x+10$
$⇒ -2x - (-6) - 8 = 5x + 10$
$⇒ -2x + 6 + (-8) = 5x+10$
$⇒ -2x -2 = 5x + 10$
$⇒ -2x - 5x = 10 + 2$
$⇒ -7x = 12$
$⇒ x = \dfrac{-12}{7}$