Question

Solve the following equation and also check your result :

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

Answer 1

\[x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3}\]
\[\text{ or }\frac{2x - x + 1}{2} = \frac{3 - x + 2}{3}\]
\[\text{ or }\frac{x + 1}{2} = \frac{5 - x}{3}\]
\[\text{ or }3x + 3 = 10 - 2x\]
\[\text{ or }5x = 10 - 3\]
\[\text{ or }x = \frac{7}{5}\]
Check: 
\[\text{ L . H . S . }= \frac{7}{5} - \frac{\frac{7}{5} - 1}{2} = \frac{7}{5} - \frac{1}{5} = \frac{6}{5}\]
\[\text{ R . H . S . }= 1 - \frac{\frac{7}{5} - 2}{3} = 1 - \frac{- 3}{15} = \frac{6}{5}\]
∴  L.H.S. = R.H.S. for x = \[\frac{7}{5}\]