Question

Solve the following equation and also check your result:
\[\frac{3a - 2}{3} + \frac{2a + 3}{2} = a + \frac{7}{6}\]

Answer 1

\[\frac{3a - 2}{3} + \frac{2a + 3}{2} = a + \frac{7}{6}\]
\[\text{ or }\frac{6a - 4 + 6a + 9}{6} = a + \frac{7}{6}\]
\[\text{ or }12a + 5 = 6a + 7\]
\[\text{ or }6a = 7 - 5\]
\[\text{ or }a = \frac{2}{6} = \frac{1}{3}\]
Check: 
\[\text{ L . H . S . }= \frac{3 \times \frac{1}{3} - 2}{3} + \frac{2 \times \frac{1}{3} + 3}{2} = \frac{- 1}{3} + \frac{11}{6} = \frac{9}{6} = \frac{3}{2}\]
\[\text{ R . H . S .} = \frac{1}{3} + \frac{7}{6} = \frac{9}{6} = \frac{3}{2}\]

∴  L.H.S. = R.H.S. for a = \[\frac{1}{3}\]