Question

Solve the following equation and also check your result:

\[\frac{3x}{4} - \frac{(x - 1)}{2} = \frac{(x - 2)}{3}\]

Answer 1

\[\frac{3x}{4} - \frac{x - 1}{2} = \frac{x - 2}{3}\]
\[\text{ or }\frac{3x - 2x + 2}{4} = \frac{x - 2}{3}\]
\[\text{ or }4x - 8 = 3x + 6\]
\[\text{ or }x = 14\]
\[\text{ Check: }\]
\[\text{ L . H . S .} = \frac{3 \times 14}{4} - \frac{14 - 1}{2} = \frac{21}{2} - \frac{13}{2} = \frac{8}{2} = 4\]
\[\text{ R . H . S . }= \frac{14 - 2}{3} = \frac{12}{3} = 4\]
∴  L.H.S. = R.H.S. for x = 14