Question

Solve the following equation and verify your answer:

\[\frac{2x + 1}{3x - 2} = \frac{5}{9}\]

Answer 1

\[\frac{2x + 1}{3x - 2} = \frac{5}{9}\]

\[\text{ or }18x + 9 = 15x - 10 [\text{ After cross multiplication }]\]

\[\text{ or }18x - 15x = - 10 - 9\]

\[\text{ or }3x = - 19\]

\[\text{ or }x = \frac{- 19}{3}\]

\[\text{ Thus, }x = \frac{- 19}{3}\text{ is the solution of the given equation .} \]

\[\text{ Check: }\]

\[\text{ Substituting }x = \frac{- 19}{3}\text{ in the given equation, we get: }\]

\[\text{ L . H . S .}= \frac{2(\frac{- 19}{3}) + 1}{3(\frac{- 19}{3}) - 2} = \frac{- 38 + 3}{- 57 - 6} = \frac{- 35}{- 63} = \frac{5}{9}\]

\[\text{ R . H . S .} = \frac{5}{9}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = \frac{- 19}{3}\]