Question

Solve the following equation and verify your answer:

\[\frac{2x - (7 - 5x)}{9x - (3 + 4x)} = \frac{7}{6}\]

Answer 1

\[\frac{2x - (7 - 5x)}{9x - (3 + 4x)} = \frac{7}{6}\]

\[\text{ or }\frac{7x - 7}{5x - 3} = \frac{7}{6}\]

\[\text{ or }42x - 42 = 35x - 21 [\text{ After cross multiplication }]\]

\[\text{ or }42x - 35x = - 21 + 42\]

\[\text{ or }7x = 21\]

\[\text{ or }x = \frac{21}{7}\]

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

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

\[\text{ Check: }\]

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

\[\text{ L . H . S . }= \frac{2 \times 3 - (7 - 5 \times 3)}{9 \times 3 - (3 + 4 \times 3)} = \frac{6 - (7 - 15)}{27 - (3 + 12)} = \frac{6 + 8}{27 - 15} = \frac{14}{12} = \frac{7}{6}\]

\[\text{ R . H . S . }= \frac{7}{6}\]

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