Question

Solve the following equation and verify your answer:

\[\frac{2x - 3}{3x + 2} = - \frac{2}{3}\]

Answer 1

\[\frac{2x - 3}{3x + 2} = - \frac{2}{3}\]

\[\text{ or }6x - 9 = - 6x - 4 (\text{ After cross multiplication })\]

\[\text{ or }6x + 6x = - 4 + 9\]

\[\text{ or }x = \frac{5}{12}\]

\[ \therefore x = \frac{5}{12}\text{ is the solution of the given equation .} \]

\[\text{ Check: }\]

\[\text{ L . H . S . }= \frac{2 \times \frac{5}{12} - 3}{3 \times \frac{5}{12} + 2} = \frac{\frac{5}{6} - 3}{\frac{5}{4} + 2} = \frac{\frac{- 13}{6}}{\frac{13}{4}} = \frac{- 4}{6} = \frac{- 2}{3}\]

\[\text{ R . H . S . }= \frac{- 2}{3}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = \frac{5}{12}\]