Question

Solve each of the following equation and also check your result in each case:
\[\frac{5x}{3} - \frac{(x - 1)}{4} = \frac{(x - 3)}{5}\]

Answer 1

\[\frac{5x}{3} - \frac{x - 1}{4} = \frac{x - 3}{5}\]
\[\text{ or }\frac{20x - 3x + 3}{12} = \frac{x - 3}{5}\]
\[\text{ or }\frac{17x + 3}{12} = \frac{x - 3}{5}\]
\[\text{ or }85x + 15 = 12x - 36\]
\[\text{ or }73x = - 51\]
\[\text{ or }x = \frac{- 51}{73}\]
\[\text{ Check: }\]
\[\text{ L . H . S . }= \frac{5 \times \frac{- 51}{73}}{3} - \frac{\frac{- 51}{73} - 1}{4} = \frac{- 255}{219} - \frac{- 124}{292} = \frac{- 54}{73}\]
\[\text{ R . H . S . }= \frac{\frac{- 51}{73} - 3}{5} = \frac{- 54}{73}\]
∴  L.H.S. = R.H.S. for x = \[\frac{- 51}{73}\]