Question

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

Answer 1

$$\begin{gathered} \frac{2-\mathrm{y}}{\mathrm{y}+7}=\frac{3}{5} \\ \mathrm{or}10-5\mathrm{y}=3\mathrm{y}+21(\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}) \\ \mathrm{or}3\mathrm{y}+5\mathrm{y}=10-21 \\ \mathrm{or}8\mathrm{y}=-11 \\ \mathrm{or}\mathrm{y}=\frac{-11}{8} \\ \therefore \mathrm{y}=\frac{-11}{8}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\text{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{y}=\frac{-11}{8}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{2-\frac{-11}{8}}{\frac{-11}{8}+7}=\frac{16+11}{-11+56}=\frac{27}{45}=\frac{3}{5} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{3}{5} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{y}=\frac{-11}{8} \end{gathered}$$