Question

Solve the following equations and verify your answer :

$\frac{2x}{3x+1}=-3$

Answer 1

$\frac{2x}{3x+1}=-3$
By cross multiplication :
$2x=-3(3x+1)\Rightarrow 2x=-9x-3$
$\Rightarrow 2x+9x=-3$ (By transposition)
$\Rightarrow 11x=-3\Rightarrow x=\frac{-3}{11}\therefore x=\frac{-3}{11}$
Verification :
$L.H.S=\frac{2x}{3x+1}=\frac{2\times \left(\frac{-3}{11}\right)}{3\left(\frac{-3}{11}\right)+1}=\frac{\frac{-6}{11}}{\frac{-9}{11}+1}=\frac{\frac{-6}{11}}{\frac{-9+11}{11}}=\frac{\frac{-6}{11}}{\frac{2}{11}}=\frac{-6}{11}\times \frac{11}{2}=\frac{-3}{1}=R.H.S.$