Question

Solve the following equation and also check your result:
\[5\left( \frac{7x + 5}{3} \right) - \frac{23}{3} = 13 - \frac{4x - 2}{3}\]

Answer 1

\[5(\frac{7x + 5}{3}) - \frac{23}{3} = 13 - \frac{4x - 2}{3}\]
\[\text{ or }\frac{35x + 25}{3} + \frac{4x - 2}{3} = 13 + \frac{23}{3}\]
\[\text{ or }\frac{35x + 25 + 4x - 2}{3} = \frac{39 + 23}{3} \]
\[\text{ or }39x + 23 = 62 [\text{ Multiplying both sides by } 3]\]
\[\text{ or }39x = 62 - 23\]
\[\text{ or }x = \frac{39}{39}\]
\[\text{ or }x = 1\]
\[\text{ Thus, }x = 1\text{ is the solution of the given equation . }\]
\[\text{ Check:} \]
\[\text{ Substituting  }x = 1\text{ in the given equation, we get: }\]
\[\text{ L . H . S . }= 5(\frac{7 \times 1 + 5}{3}) - \frac{23}{3} = \frac{60}{3} - \frac{23}{3} = \frac{37}{3}\]
\[\text{ R . H . S . }= 13 - \frac{4 \times 1 - 2}{3} = \frac{39 - 2}{3} = \frac{37}{3}\]
\[ \therefore\text{ L . H . S . = R . H . S . for }x = 1 .\]