Question

Solve the following equations and verify your answer :

$\frac{6}{2x-(3-4x)}=\frac{2}{3}$

Answer 1

$\frac{6}{2x-(3-4x)}=\frac{2}{3}\Rightarrow \frac{6}{2x-3+4x}=\frac{2}{3}\Rightarrow \frac{6}{6x-3}=\frac{2}{3}$
By cross multiplication :
$2(6x-3)=6\times 3\Rightarrow 12x=24\Rightarrow x=\frac{24}{12}=2\therefore x=2$
Verification :
$L.H.S.=\frac{6}{2x-(3-4x)}=\frac{6}{2\times 2-(3-4\times 2)}=\frac{6}{4-(3-8)}=\frac{6}{4+5}=\frac{6}{9}=\frac{2}{3}=R.H.S.$