Question
Solve the following equation and verify your answer: $\frac{2-\text{y}}{\text{y}+7}=\frac{3}{5}$
✓
Answer
$\frac{2\text{x}-3}{3\text{x}+2}=-\frac{2}{3}$By cross multiplication:
$3(\text{y}+7)=5(2-\text{y})$
$\Rightarrow3\text{y}+21=10-5\text{y}$
$\Rightarrow3\text{y}+5\text{y}=10-21$ (By transposition)
$\Rightarrow8\text{y}=-11$
$\Rightarrow\text{y}=\frac{-11}{8}$
$\therefore\text{y}=\frac{-11}{8}$Verification:
$\text{L.H.S.}=\frac{2-\text{y}}{\text{y}+7}=\frac{2+\frac{11}{8}}{\frac{-11}{8}+7}$
$=\frac{\frac{16+11}{8}}{\frac{-11+56}{8}}=\frac{\frac{27}{8}}{\frac{45}{8}}$
$=\frac{27}{8}\times\frac{8}{45}=\frac{27}{45}=\frac{3}{5}=\text{R.H.S.}$
$3(\text{y}+7)=5(2-\text{y})$
$\Rightarrow3\text{y}+21=10-5\text{y}$
$\Rightarrow3\text{y}+5\text{y}=10-21$ (By transposition)
$\Rightarrow8\text{y}=-11$
$\Rightarrow\text{y}=\frac{-11}{8}$
$\therefore\text{y}=\frac{-11}{8}$Verification:
$\text{L.H.S.}=\frac{2-\text{y}}{\text{y}+7}=\frac{2+\frac{11}{8}}{\frac{-11}{8}+7}$
$=\frac{\frac{16+11}{8}}{\frac{-11+56}{8}}=\frac{\frac{27}{8}}{\frac{45}{8}}$
$=\frac{27}{8}\times\frac{8}{45}=\frac{27}{45}=\frac{3}{5}=\text{R.H.S.}$
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