Question

Solve the following equation and verify your answer:
$\frac{6}{2x-(3-4x)}=\frac{2}{3}$

Answer 1

$$\begin{gathered} \frac{6}{2\mathrm{x}-(3-4\mathrm{x})}=\frac{2}{3} \\ \mathrm{or}\frac{6}{6\mathrm{x}-3}=\frac{2}{3} \\ \mathrm{or}12\mathrm{x}-6=18[\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{or}12\mathrm{x}=18+6 \\ \mathrm{or}\mathrm{x}=\frac{24}{12} \\ \mathrm{or}\mathrm{x}=2 \\ \mathrm{Thus},\mathrm{x}=2\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=2\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{6}{2\times 2-(3-4\times 2)}=\frac{6}{9}=\frac{2}{3} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{2}{3} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=2. \end{gathered}$$