Question

Solve the following equation and also check your result:
\[\frac{1}{2}x + 7x - 6 = 7x + \frac{1}{4}\]

Answer 1

\[\frac{1}{2}x + 7x - 6 = 7x + \frac{1}{4}\]
\[\text{ or }\frac{1}{2}x + 7x - 7x = \frac{1}{4} + 6\]
\[\text{ or }\frac{x}{2} = \frac{1 + 24}{4}\]
\[\text{ or }\frac{x}{2} = \frac{25}{4}\]
\[\text{ or }x = \frac{25}{2}\]
Check:
\[\text{ L . H . S . }= \frac{1}{2} \times \frac{25}{2} + 7 \times \frac{25}{2} - 6 = \frac{351}{4}\]
\[\text{ R . H . S . }= 7 \times \frac{25}{2} + \frac{1}{4} = \frac{351}{4}\]
∴  L.H.S. = R.H.S. for x = \[\frac{25}{2}\]