Question

Solve the following equation and also verify your solution:

\[\frac{x}{2} - \frac{4}{5} + \frac{x}{5} + \frac{3x}{10} = \frac{1}{5}\]

Answer 1

\[\frac{x}{2} - \frac{4}{5} + \frac{x}{5} + \frac{3x}{10} = \frac{1}{5}\]
\[\text{ or }\frac{x}{2} + \frac{x}{5} + \frac{3x}{10} = \frac{1}{5} + \frac{4}{5}\]
\[\text{ or }\frac{5x + 2x + 3x}{10} = \frac{5}{5}\]
\[\text{ or }\frac{10x}{10} = 1\]
\[\text{ or }x = 1\]
\[\text{ Verification: }\]
\[\text{ L . H . S . }= \frac{1}{2} - \frac{4}{5} + \frac{1}{5} + \frac{3}{10}\]
\[ = \frac{5 - 8 + 2 + 3}{10} = \frac{1}{5} =\text{ R . H . S .}\]