Question

Solve the following equation and also verify your solution:
\[\frac{2}{3}(x - 5) - \frac{1}{4}(x - 2) = \frac{9}{2}\]

Answer 1

\[\frac{2}{3}(x - 5) - \frac{1}{4}(x - 2) = \frac{9}{2}\]
\[\text{or }\frac{2x - 10}{3} - \frac{x - 2}{4} = \frac{9}{2}\]
\[\text{ or }\frac{8x - 40 - 3x + 6}{12} = \frac{9}{2}\]
\[\text{ or }\frac{5x - 34}{12} = \frac{9}{2}\]
\[\text{ or }10x - 68 = 108\]
\[\text{ or }10x = 108 + 68\]
\[\text{ or }x = \frac{176}{10} = \frac{88}{5}\]
\[\text{ Verification: }\]
\[\text{ L . H . S . }= \frac{2}{3}(\frac{88}{5} - 5) - \frac{1}{4}(\frac{88}{5} - 2)\]
\[ = \frac{2}{3} \times \frac{63}{5} - \frac{1}{4} \times \frac{78}{5} = \frac{9}{2} = \text{ R . H . S .}\]