Question
Solve the following equation and verify your answer: $\frac{5\text{x}-7}{3\text{x}}=2$
✓
Answer
$\frac{5\text{x}-7}{3\text{x}}=\frac{2}{1}$By cross multiplication:
$2\times3\text{x}=5\text{x}-7$
$\Rightarrow6\text{x}-5\text{x}=-7$
$\Rightarrow\text{x}=-7$ (By transposition) $\therefore\text{x}=-7$Verification:
$\text{L.H.S.}=\frac{5\text{x}-7}{3\text{x}}=\frac{5\times(-7)-7}{3(-7)}$
$=\frac{-35-7}{-21}=\frac{-42}{-21}=\frac{2}{1}=\text{R.H.S.}$
$2\times3\text{x}=5\text{x}-7$
$\Rightarrow6\text{x}-5\text{x}=-7$
$\Rightarrow\text{x}=-7$ (By transposition) $\therefore\text{x}=-7$Verification:
$\text{L.H.S.}=\frac{5\text{x}-7}{3\text{x}}=\frac{5\times(-7)-7}{3(-7)}$
$=\frac{-35-7}{-21}=\frac{-42}{-21}=\frac{2}{1}=\text{R.H.S.}$
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