Question

Solve the following equation and also check your result :
\[\frac{6x + 1}{2} + 1 = \frac{7x - 3}{3}\]

Answer 1

\[\frac{6x + 1}{2} + 1 = \frac{7x - 3}{3}\]
\[\text{ or }\frac{6x + 1 + 2}{2} = \frac{7x - 3}{3}\]
\[\text{ or }18x + 9 = 14x - 6\]
\[\text{ or }18x - 14x = - 6 - 9\]
\[\text{ or }4x = - 15\]
\[\text{ or }x = \frac{- 15}{4}\]
Check: 
\[\text{ L . H . S .} = \frac{6 \times \frac{- 15}{4} + 1}{2} + 1 = \frac{- 45 + 2 + 4}{4} = \frac{- 39}{4}\]
\[\text{ R . H . S . }= \frac{7 \times \frac{- 15}{4} - 3}{3} = \frac{- 105 - 12}{12} = \frac{- 39}{4}\]
∴  L.H.S. = R.H.S. for x = \[\frac{- 15}{4}\]