Question

Solve the following equation and verify your answer:

\[\frac{6}{2x - (3 - 4x)} = \frac{2}{3}\]

Answer 1

\[\frac{6}{2x - (3 - 4x)} = \frac{2}{3}\]

\[\text{ or }\frac{6}{6x - 3} = \frac{2}{3}\]

\[\text{ or }12x - 6 = 18 [\text{ After cross multiplication }]\]

\[\text{ or }12x = 18 + 6\]

\[\text{ or }x = \frac{24}{12}\]

\[\text{ or }x = 2\]

\[\text{ Thus, }x = 2\text{ is the solution of the given equation . }\]

\[\text{ Check: }\]

\[\text{ Substituting }x = 2\text{ in the given equation, we get: }\]

\[\text{ L . H . S . }= \frac{6}{2 \times 2 - (3 - 4 \times 2)} = \frac{6}{9} = \frac{2}{3}\]

\[\text{ R . H . S . }= \frac{2}{3}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = 2 .\]