Question
Solve the following equation and verify your answer:
$\frac{2\text{x}}{3\text{x}+1}=-3$
$\frac{2\text{x}}{3\text{x}+1}=-3$
✓
Answer
$\frac{2\text{x}}{3\text{x}+1}=\frac{-3}{1}$By cross multiplication:
$2\text{x}=-3(3\text{x}+1)$ $\Rightarrow2\text{x}+9\text{x}=-3$ (By transposition) $\Rightarrow11\text{x}=-3$ $\Rightarrow\text{x}=\frac{-3}{11}$ $\therefore\text{x}=\frac{-3}{11}$Verification:
$\text{L.H.S.}=\frac{2\text{x}}{3\text{x}+1}=\frac{2\times\Big(\frac{-3}{11}\Big)}{3\Big(\frac{-3}{11}\Big)+1}=\frac{\frac{-6}{11}}{\frac{-9}{11}+1}$ $=\frac{\frac{-6}{11}}{\frac{-9+11}{11}}=\frac{\frac{-6}{11}}{\frac{2}{11}}=\frac{-6}{11}\times\frac{11}{2}$ $\frac{-3}{1}=\text{R.H.S.}$
$2\text{x}=-3(3\text{x}+1)$ $\Rightarrow2\text{x}+9\text{x}=-3$ (By transposition) $\Rightarrow11\text{x}=-3$ $\Rightarrow\text{x}=\frac{-3}{11}$ $\therefore\text{x}=\frac{-3}{11}$Verification:
$\text{L.H.S.}=\frac{2\text{x}}{3\text{x}+1}=\frac{2\times\Big(\frac{-3}{11}\Big)}{3\Big(\frac{-3}{11}\Big)+1}=\frac{\frac{-6}{11}}{\frac{-9}{11}+1}$ $=\frac{\frac{-6}{11}}{\frac{-9+11}{11}}=\frac{\frac{-6}{11}}{\frac{2}{11}}=\frac{-6}{11}\times\frac{11}{2}$ $\frac{-3}{1}=\text{R.H.S.}$
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