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Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

Solve the fol...

Question

Solve the following equations and verify your answer :

$\frac{2 x}{3 x + 1} = - 3$

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Solution

$\frac{2 x}{3 x + 1} = - 3$
By cross multiplication :
$2 x = - 3 (3 x + 1) \Rightarrow 2 x = - 9 x - 3$
$\Rightarrow 2 x + 9 x = - 3$ (By transposition)
$\Rightarrow 11 x = - 3 \Rightarrow x = \frac{- 3}{11} ∴ x = \frac{- 3}{11}$
Verification :
$L . H . S = \frac{2 x}{3 x + 1} = \frac{2 \times (\frac{- 3}{11})}{3 (\frac{- 3}{11}) + 1} = \frac{\frac{- 6}{11}}{\frac{- 9}{11} + 1} = \frac{\frac{- 6}{11}}{\frac{- 9 + 11}{11}} = \frac{\frac{- 6}{11}}{\frac{2}{11}} = \frac{- 6}{11} \times \frac{11}{2} = \frac{- 3}{1} = R . H . S .$

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