Question

Solve the following equations and verify your answer :

$\frac{2x-3}{3x+2}=-\frac{2}{3}$

Answer 1

$\frac{2x-3}{3x+2}=-\frac{2}{3}$

By cross multiplication :

$3(2x-3)=-2(3x+2)$

$\Rightarrow 6x-9=-6x-4$

$\Rightarrow 6x+6x=-4+9$ (By transposition)

$\Rightarrow 12x=5\Rightarrow x=\frac{5}{12}$

$\therefore x=\frac{5}{12}$

Verification :

$L.H.S.=\frac{2x-3}{3x+2}=\frac{2\times \frac{5}{12}-3}{3\times \frac{5}{12}+2}=\frac{\frac{5}{6}-3}{\frac{5}{4}+2}=\frac{\frac{5-18}{6}}{\frac{5+8}{4}}=\frac{-13}{6}\times \frac{4}{13}=\frac{-2}{3}=R.H.S.$