Question

Solve the following equation and also check your result:

\[\frac{3}{4}x + 4x = \frac{7}{8} + 6x - 6\]

Answer 1

\[\frac{3}{4}x + 4x = \frac{7}{8} + 6x - 6\]
\[\text{ or }\frac{3}{4}x - 2x = \frac{7}{8} - 6\]
\[\text{ or }\frac{3x - 8x}{4} = \frac{7 - 48}{8}\]
\[\text{ or }\frac{- 5x}{4} = \frac{- 41}{8}\]
\[\text{ or }- 40x = - 164\]
\[\text{ or }x = \frac{- 164}{- 40} = \frac{41}{10}\]
\[\text{ Check: }\]
\[\text{ L . H . S . }= \frac{3}{4} \times \frac{41}{10} + 4 \times \frac{41}{10} = \frac{123}{40} + \frac{164}{10} = \frac{123 + 656}{40} = \frac{779}{40}\]
\[\text{ R . H . S .} = \frac{7}{8} + 6 \times \frac{41}{10} - 6 = \frac{7}{8} + \frac{246}{10} - 6 = \frac{35 + 984 - 240}{40} = \frac{779}{40}\]
∴ L.H.S. = R.H.S. for x =\[\frac{41}{10}\]