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Performing Mathematical Operations on Equation

Solve:5 x-13x...

Question

Solve:
$5 x - \frac{1}{3} (x + 1) = 6 (x + \frac{1}{30})$

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Solution

$5 x - \frac{1}{3} (x + 1) = 6 (x + \frac{1}{30}) \Rightarrow 5 x - \frac{1 (x + 1)}{3} = 6 (\frac{30 x + 1}{30}) (L . C . M . of 1 and 30 is 30) \Rightarrow 5 x - \frac{(x + 1)}{3} = \frac{30 x + 1}{5} \Rightarrow \frac{15 x - x - 1}{3} = \frac{30 x + 1}{5} (L . C . M . of 1 and 3 is 3) \Rightarrow \frac{14 x - 1}{3} = \frac{30 x + 1}{5} \Rightarrow 5 (14 x - 1) = 3 (30 x + 1) (by cross multiplication) \Rightarrow 70 x - 5 = 90 x + 3 \Rightarrow 70 x - 90 x = 3 + 5 \Rightarrow - 20 x = 8 \Rightarrow x = \frac{8}{- 20} = \frac{- 2}{5} ∴ x = - \frac{2}{5}$

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