Question

Solve the following equation and verify your answer:
$\frac{3x+5}{2x+7}=4$

Answer 1

$$\begin{gathered} \frac{3\mathrm{x}+5}{2\mathrm{x}+7}=4 \\ \mathrm{or}3\mathrm{x}+5=8\mathrm{x}+28 \\ \mathrm{or}8\mathrm{x}+28=3\mathrm{x}+5(\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}) \\ \mathrm{or}8\mathrm{x}-3\mathrm{x}=5-28 \\ \mathrm{or}5\mathrm{x}=-23 \\ \mathrm{or}\mathrm{x}=\frac{-23}{5} \\ \therefore \mathrm{x}=\frac{-23}{5}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=\frac{-23}{5}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{3\times {\displaystyle \frac{-23}{5}}+5}{2\times {\displaystyle \frac{-23}{5}}+7}=\frac{-69+25}{-46+35}=\frac{-44}{-11}=4 \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=4 \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=\frac{-23}{5} \end{gathered}$$