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Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equations:
$\frac{18 (7 x - 3)}{2 x + 1} = \frac{250 \sqrt{2 x + 1}}{3 \sqrt{7 x - 3}}$ .

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Solution

$\frac{18 (7 x - 3)}{2 x + 1} = \frac{250 \sqrt{2 x + 1}}{3 \sqrt{7 x - 3}} 54 (7 x - 3) \sqrt{7 x - 3} = 250 (2 x + 1) \sqrt{2 x + 1} 27 (7 x - 3) \sqrt{7 x - 3} = 125 (2 x + 1) \sqrt{2 x + 1}$
Squaring both sides
$729 {(7 x - 3)}^{3} = 15625 {(2 x + 1)}^{3} 9^{3} {(7 x - 3)}^{3} = {(25)}^{3} {(2 x + 1)}^{3}$
Taking cube root on both sides
$9 (7 x - 3) = 25 (2 x + 1) 63 x - 27 = 50 x + 25 13 x = 52 x = 4$

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Solving Equations with Variables on Both Sides

Standard VIII Mathematics

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