Question

Solve the following equation and verify your answer:
$\frac{(2x+3)-(5x-7)}{6x+11}=-\frac{8}{3}$

Answer 1

$$\begin{gathered} \frac{(2\mathrm{x}+3)-(5\mathrm{x}-7)}{6\mathrm{x}+11}=\frac{-8}{3} \\ \mathrm{or}\frac{-3\mathrm{x}+10}{6\mathrm{x}+11}=\frac{-8}{3} \\ \mathrm{or}-9\mathrm{x}+30=-48\mathrm{x}-88[\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{or}-9\mathrm{x}+48\mathrm{x}=-88-30 \\ \mathrm{or}39\mathrm{x}=-118\mathrm{or}\mathrm{x}=\frac{-118}{39} \\ \mathrm{Thus},\mathrm{x}=\frac{-118}{39}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=\frac{-118}{39}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{-3\left(\frac{-118}{39}\right)+10}{6\left(\frac{-118}{39}\right)+11}=\frac{354+390}{-708+429}=\frac{744}{-279}=\frac{-8}{-3} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{-8}{3} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=\frac{-118}{39} \end{gathered}$$