Question

Solve the following equation and verify your answer:

\[\frac{(2x + 3) - (5x - 7)}{6x + 11} = - \frac{8}{3}\]

Answer 1

\[\frac{(2x + 3) - (5x - 7)}{6x + 11} = \frac{- 8}{3}\]

\[\text{ or }\frac{- 3x + 10}{6x + 11} = \frac{- 8}{3}\]

\[\text{ or }- 9x + 30 = - 48x - 88 [\text{ After cross multiplication }]\]

\[\text{ or }- 9x + 48x = - 88 - 30\]

\[\text{ or }39x=-118\text{ or }x=\frac{- 118}{39}\]

\[\text{ Thus, }x = \frac{- 118}{39}\text{ is the solution of the given equation .} \]

\[\text{ Check: }\]

\[\text{ Substituting }x = \frac{- 118}{39}\text{ in the given equation, we get: }\]

\[\text{ L . H . S . }= \frac{- 3(\frac{- 118}{39}) + 10}{6(\frac{- 118}{39}) + 11} = \frac{354 + 390}{- 708 + 429} = \frac{744}{- 279} = \frac{- 8}{- 3}\]

\[\text{ R . H . S .} = \frac{- 8}{3}\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = \frac{- 118}{39}\]