Question

Solve the following equation and verify your answer:

\[\frac{3x + 5}{4x + 2} = \frac{3x + 4}{4x + 7}\]

Answer 1

\[\frac{3x + 5}{4x + 2} = \frac{3x + 4}{4x + 7}\]

\[\text{ or, }12 x^2 + 20x + 21x + 35 = 12 x^2 + 16x + 6x + 8 [\text{ Cross multiply }]\]

\[\text{ or, }12 x^2 - 12 x^2 + 41x - 22x = 8 - 35\]

\[\text{ or, }19x = - 27\]

\[\text{ or, }x = \frac{- 27}{19}\]

\[\text{ Thus, }x = \frac{- 27}{19}\text{ is the solution of the given equation }\]

\[\text{ Check: }\]

\[\text{ Substituting }x = \frac{- 27}{19}\text{ in the given equation, we get: }\]

\[\text{ L . H . S . }= \frac{3(\frac{- 27}{19}) + 5}{4(\frac{- 27}{19}) + 2} = \frac{- 81 + 95}{- 108 + 38} = \frac{14}{- 70} = \frac{- 1}{5}\]

\[\text{ R . H . S . }= \frac{3(\frac{- 27}{19}) + 4}{4(\frac{- 27}{19}) + 7} = \frac{- 81 + 76}{- 108 + 133} = \frac{- 5}{25} = \frac{- 1}{5}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = \frac{- 27}{19}\]