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Equations Reducible to the Linear Form

Question 62So...

Question

Question 62

Solve the following:

$\frac{x}{2} - \frac{1}{4} (x - \frac{1}{3}) = \frac{1}{6} (x + 1) + \frac{1}{12}$

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Solution

Given, $\frac{x}{2} - \frac{1}{4} (x - \frac{1}{3}) = \frac{1}{6} (x + 1) + \frac{1}{12}$
$\Rightarrow \frac{x}{2} - \frac{x}{4} + \frac{1}{12} = \frac{x}{6} + \frac{1}{6} + \frac{1}{12} \Rightarrow \frac{2 x - x}{4} + \frac{1}{12} = \frac{x}{6} + \frac{2 + 1}{12} \Rightarrow \frac{x}{4} + \frac{1}{12} = \frac{x}{6} + \frac{3}{12} \Rightarrow \frac{x}{4} - \frac{x}{6} = \frac{3}{12} - \frac{1}{12} \Rightarrow \frac{3 x - 2 x}{12} = \frac{3 - 1}{12} \Rightarrow \frac{x}{12} = \frac{2}{12} \Rightarrow 12 x = 2 \times 12 \Rightarrow 12 x = 24 \Rightarrow \frac{12 x}{12} = \frac{24}{12} ∴ x = 2$

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Equations Reducible to the Linear Form

Standard VIII Mathematics

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