Solve the following equation and verify your answer: 2x 3x+1 =-3 - Vidyadip

Question

Solve the following equation and verify your answer: $\frac{2\text{x}}{3\text{x}+1}=-3$

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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:
$\text{L.H.S.}=\frac{2\text{x}}{3\text{x}+1}=\frac{2\times\Big(\frac{-3}{11}\Big)}{3\Big(\frac{-3}{11}\Big)+1}=\frac{\frac{-6}{11}}{\frac{-9}{11}+1}$
$=\frac{\frac{-6}{11}}{\frac{-9+11}{11}}=\frac{\frac{-6}{11}}{\frac{2}{11}}=\frac{-6}{11}\times\frac{11}{2}$
$\frac{-3}{1}=\text{R.H.S.}$

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