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Solving Equations with Variables on Both Sides

Solve each of...

Question

Solve each of the following equations and also check your result in each case :

$\frac{2 x + 5}{3} = 3 x - 10$

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Solution

$\frac{2 x + 5}{3} = \frac{3 x - 10}{1}$
By cross multiplication:
2x+5=3(3x-10)
2x+5=9x-30
5+30=9x-2x (By transposition)
$\Rightarrow 35 = 7 x \Rightarrow x = \frac{35}{7} = 5 ∴ x = 5 L . H . S = \frac{2 x + 5}{3} = \frac{2 \times 5 + 5}{3} = \frac{10 + 5}{3} = \frac{15}{3} = 5 R . H . S . = 3 x - 10 = 3 \times 5 - 10 = 15 - 10 = 5 ∴ L . H . S = R . H . S$

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Solving Equations with Variables on Both Sides

Standard VIII Mathematics

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