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प्रश्न
Solve the following equation and verify your answer:
\[\frac{2x + 1}{3x - 2} = \frac{5}{9}\]
योग
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उत्तर
\[\frac{2x + 1}{3x - 2} = \frac{5}{9}\]
\[\text{ or }18x + 9 = 15x - 10 [\text{ After cross multiplication }]\]
\[\text{ or }18x - 15x = - 10 - 9\]
\[\text{ or }3x = - 19\]
\[\text{ or }x = \frac{- 19}{3}\]
\[\text{ Thus, }x = \frac{- 19}{3}\text{ is the solution of the given equation .} \]
\[\text{ Check: }\]
\[\text{ Substituting }x = \frac{- 19}{3}\text{ in the given equation, we get: }\]
\[\text{ L . H . S .}= \frac{2(\frac{- 19}{3}) + 1}{3(\frac{- 19}{3}) - 2} = \frac{- 38 + 3}{- 57 - 6} = \frac{- 35}{- 63} = \frac{5}{9}\]
\[\text{ R . H . S .} = \frac{5}{9}\]
\[ \therefore\text{ L . H . S . = R . H . S . for }x = \frac{- 19}{3}\]
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