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Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equation:

$\frac{x - 1}{7 x - 14} = \frac{x - 3}{7 x - 26}$

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Solution

$\frac{x - 1}{7 x - 14} = \frac{x - 3}{7 x - 26} \Rightarrow (x - 1) (7 x - 26) = (7 x - 14) (x - 3) \Rightarrow 7 x^{2} - 7 x - 26 x + 26 = 7 x^{2} - 14 x - 21 x + 42 \Rightarrow - 33 x + 26 = - 35 x + 4 x \Rightarrow 35 x - 33 x = 42 - 26 \Rightarrow 2 x = 16 \Rightarrow x = 8$

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Solving Equations with Variables on Both Sides

Standard VIII Mathematics

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