Question
Solve the following equation and verify your answer:
$\frac{3\text{x}+5}{2\text{x}+7}=4$
$\frac{3\text{x}+5}{2\text{x}+7}=4$
✓
Answer
$\frac{3\text{x}+5}{2\text{x}+7}=\frac{4}{1}$By cross multiplication:
$4(2\text{x}+7)=1\times(3\text{x}+5)$ $8\text{x}+28=3\text{x}+5$ $8\text{x}-3\text{x}=5-28$ (By transposition) $\Rightarrow5\text{x}=-23$ $\Rightarrow\text{x}=\frac{-23}{5}$ $\text{x}=\frac{-23}{5}$Verification:
$\text{L.H.S.}=\frac{3\text{x}+5}{2\text{x}+7}=\frac{3\Big(\frac{-23}{5}\Big)+5}{2\Big(\frac{-23}{5}\Big)+7}$ $=\frac{\frac{-69}{5}+5}{\frac{-46}{5}+7}=\frac{\frac{-69+25}{5}}{\frac{-46+35}{5}}=\frac{\frac{-44}{5}}{\frac{-11}{5}}$ $\frac{-44}{5}\times\frac{-5}{11}=4=\text{R.H.S.}$
$4(2\text{x}+7)=1\times(3\text{x}+5)$ $8\text{x}+28=3\text{x}+5$ $8\text{x}-3\text{x}=5-28$ (By transposition) $\Rightarrow5\text{x}=-23$ $\Rightarrow\text{x}=\frac{-23}{5}$ $\text{x}=\frac{-23}{5}$Verification:
$\text{L.H.S.}=\frac{3\text{x}+5}{2\text{x}+7}=\frac{3\Big(\frac{-23}{5}\Big)+5}{2\Big(\frac{-23}{5}\Big)+7}$ $=\frac{\frac{-69}{5}+5}{\frac{-46}{5}+7}=\frac{\frac{-69+25}{5}}{\frac{-46+35}{5}}=\frac{\frac{-44}{5}}{\frac{-11}{5}}$ $\frac{-44}{5}\times\frac{-5}{11}=4=\text{R.H.S.}$
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