Question

Solve each of the following equation and also check your result in each case:
\[\frac{(1 - 2x)}{7} - \frac{(2 - 3x)}{8} = \frac{3}{2} + \frac{x}{4}\]

Answer 1

\[\frac{1 - 2x}{7} - \frac{2 - 3x}{8} = \frac{3}{2} + \frac{x}{4}\]
\[\text{ or }\frac{1 - 2x}{7} = \frac{3}{2} + \frac{x}{4} + \frac{2 - 3x}{8}\]
\[\text{ or }\frac{1 - 2x}{7} = \frac{12 + 2x + 2 - 3x}{8}\]
\[\text{ or }\frac{1 - 2x}{7} = \frac{14 - x}{8}\]
\[\text{ or }8 - 16x = 98 - 7x\]
\[\text{ or }- 16x + 7x = 98 - 8\]
\[\text{ or }x = \frac{- 90}{9}\]
\[ = - 10\]
\[\text{ Check: }\]
\[\text{ L . H . S .} = \frac{1 - 2 \times \left( - 10 \right)}{7} - \frac{2 - 3 \times \left( - 10 \right)}{8} = \frac{1 + 20}{7} - \frac{2 + 30}{8} = 3 - 4 = - 1\]
\[\text{ R . H . S . }= \frac{3}{2} + \frac{- 10}{4} = \frac{3}{2} + \frac{- 5}{2} = \frac{3 - 5}{2} = - 1\]
∴  L.H.S. = R.H.S. for x = -10