Question

Solve the following equation and also check your result:

\[\frac{9x + 7}{2} - \left( x - \frac{x - 2}{7} \right) = 36\]

Answer 1

\[\frac{9x + 7}{2} - (x - \frac{x - 2}{7}) = 36\]
\[\text{ or }\frac{63x + 49 - 14x + 2x - 4}{14} = 36\]
\[\text{ or }\frac{51x + 45}{14} = 36\]
\[\text{ or }51x + 45 = 504\]
\[\text{ or }51x = 504 - 45\]
\[\text{ or }x = \frac{459}{51} = 9\]
\[\text{ Thus, }x = 9 \text{ is the solution of the given equation}. \]
\[\text{ Check: }\]
\[\text{ Substituting }x = 9\text{ in the given equation, we get: }\]
\[\text{ L . H . S . }= \frac{9 \times 9 + 7}{2} - (9 - \frac{9 - 2}{7}) = \frac{88}{2} - 9 + \frac{7}{7} = 44 - 9 + 1 = 36\]
\[\text{ R . H . S .} = 36\]
\[ \therefore\text{ L . H . S . = R . H . S . for }x = 9 .\]