Question

Solve the following equation and also check your result:

\[\frac{7x - 1}{4} - \frac{1}{3}\left( 2x - \frac{1 - x}{2} \right) = \frac{10}{3}\]

Answer 1

\[\frac{7x - 1}{4} - \frac{1}{3}(2x - \frac{1 - x}{2}) = \frac{10}{3}\]
\[\text{ or }\frac{7x - 1}{4} - \frac{2x}{3} + \frac{1 - x}{6} = \frac{10}{3}\]
\[\text{ or }\frac{21x - 3 - 8x + 2 - 2x}{12} = \frac{10}{3}\]
\[\text{ or }11x - 1 = 40 [\text{ Multiplying both sides by }12]\]
\[\text{ or }11x = 40 + 1\]
\[\text{ or }x = \frac{41}{11}\]
\[\text{ Thus, }x = \frac{41}{11}\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ Substituting }x = \frac{41}{11}\text{ in the given equation, we get: }\]
\[\text{ L . H . S . }= \frac{7 \times \frac{41}{11} - 1}{4} - \frac{1}{3}(2 \times \frac{41}{11} - \frac{1 - \frac{41}{11}}{2}) = \frac{276}{44} - \frac{82}{33} + \frac{- 30}{66} = \frac{10}{3}\]
\[\text{ R . H . S .} = \frac{10}{3}\]
\[ \therefore \text{ L . H . S . = R . H . S . for }x = \frac{41}{11}\]