Question

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

Answer 1

$$\begin{gathered} \frac{2\mathrm{x}-3}{3\mathrm{x}+2}=-\frac{2}{3} \\ \mathrm{or}6\mathrm{x}-9=-6\mathrm{x}-4(\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}) \\ \mathrm{or}6\mathrm{x}+6\mathrm{x}=-4+9 \\ \mathrm{or}\mathrm{x}=\frac{5}{12} \\ \therefore \mathrm{x}=\frac{5}{12}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{2\times {\displaystyle \frac{5}{12}}-3}{3\times {\displaystyle \frac{5}{12}}+2}=\frac{{\displaystyle \frac{5}{6}}-3}{{\displaystyle \frac{5}{4}}+2}=\frac{{\displaystyle \frac{-13}{6}}}{{\displaystyle \frac{13}{4}}}=\frac{-4}{6}=\frac{-2}{3} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{-2}{3} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=\frac{5}{12} \end{gathered}$$