Question

Solve the following equation and verify your answer:
$\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$

Answer 1

$$\begin{gathered} \frac{2}{3\mathrm{x}}-\frac{3}{2\mathrm{x}}=\frac{1}{12} \\ \mathrm{or},\frac{4-9}{6\mathrm{x}}=\frac{1}{12} \\ \mathrm{or},\frac{-5}{\mathrm{x}}=\frac{1}{2} \\ \mathrm{or},\mathrm{x}=-10[\text{After}c\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{Thus},\mathrm{x}=-10\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=-10\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{2}{3(-10)}-\frac{3}{2(-10)}=\frac{2}{-30}-\frac{3}{-20}=\frac{4-9}{-60}=\frac{-5}{-60}=\frac{1}{12} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{1}{12} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=-10. \end{gathered}$$