x 9x 5=57 ⇒ 7(x 9)=5(x 5) ⇒ 7x 63=5x 25 ⇒ 7x 5x= 25+63 ⇒ 2x=38 ⇒ x=382=19 ∴ x=19 ...

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Solving Equations with Variables on Both Sides

Solve: x-9x-...

Question

Solve:
$\frac{x - 9}{x - 5} = \frac{5}{7}$

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Solution

$\frac{x - 9}{x - 5} = \frac{5}{7}$
$\Rightarrow 7 (x - 9) = 5 (x - 5)$
$\Rightarrow 7 x - 63 = 5 x - 25$
$\Rightarrow 7 x - 5 x = - 25 + 63$
$\Rightarrow 2 x = 38$
$\Rightarrow x = \frac{38}{2} = 19$
$∴ x = 19$

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