Question

Solve the following equation and also verify your solution:

\[\frac{2x - 1}{3} - \frac{6x - 2}{5} = \frac{1}{3}\]

Answer 1

\[\frac{2x - 1}{3} - \frac{6x - 2}{5} = \frac{1}{3}\]
\[\text{ or }\frac{10x - 5 - 18x + 6}{15} = \frac{1}{3}\]
\[\text{ or }\frac{- 8x + 1}{15} = \frac{1}{3}\]
\[\text{ or }- 24x + 3 = 15\]
\[\text{ or }24x = 3 - 15\]
\[\text{ or }x = \frac{- 12}{24} = \frac{- 1}{2}\]
\[\text{ Verification: }\]
\[\text{ L . H . S . }= \frac{2 \times \frac{- 1}{2} - 1}{3} - \frac{6 \times \frac{- 1}{2} - 2}{5}\]
\[ = \frac{- 2}{3} - \frac{- 5}{5}\]
\[ = \frac{- 2 + 3}{3} = \frac{1}{3} =\text{ R . H . S .}\]