Question

Solve the following equation and verify your answer:

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

Answer 1

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

\[\text{ or }3x + 5 = 8x + 28\]

\[\text{ or }8x + 28 = 3x + 5 (\text{ After cross multiplication })\]

\[\text{ or }8x - 3x = 5 - 28\]

\[\text{ or }5x = - 23\]

\[\text{ or }x = \frac{- 23}{5}\]

\[ \therefore x = \frac{- 23}{5}\text{ is the solution of given equation .} \]

\[\text{ Check: }\]

\[\text{ Substituting }x = \frac{- 23}{5}\text{ in the given equation, we get: }\]

\[\text{ L . H . S .} = \frac{3 \times \frac{- 23}{5} + 5}{2 \times \frac{- 23}{5} + 7} = \frac{- 69 + 25}{- 46 + 35} = \frac{- 44}{- 11} = 4\]

\[\text{ R . H . S . }= 4\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = \frac{- 23}{5}\]