Question

Solve the following equation and also check your result:
\[6 . 5x + \frac{19 . 5x - 32 . 5}{2} = 6 . 5x + 13 + \left( \frac{13x - 26}{2} \right)\]

Answer 1

\[6 . 5x + \frac{19 . 5x - 32 . 5}{2} = 6 . 5x + 13 + \frac{13x - 26}{2}\]
\[\text{ or }\frac{19 . 5x - 32 . 5}{2} - \frac{13x - 26}{2} = 13\]
\[\text{ or }\frac{19 . 5x - 32 . 5 - 13x + 26}{2} = 13\]
\[\text{ or }6 . 5x - 6 . 5 = 26 [\text{ After cross multiplication }]\]
\[\text{ or }6 . 5x = 26 + 6 . 5\]
\[\text{ or }x = \frac{32 . 5}{6 . 5} = 5\]
\[\text{ Thus, }x = 5\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ Substituting }x = 5\text{ in the given equation, we get: }\]
\[\text{ L . H . S .} = 6 . 5 \times 5 + \frac{19 . 5 \times 5 - 32 . 5}{2} = 65\]
\[\text{ R . H . S . }= 6 . 5 \times 5 + 13 + \frac{13 \times 5 - 26}{2} = 65\]
\[ \therefore \text{ L . H . S . = R . H . S . for }x = 5 .\]