Solving equations with fractions

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Some equations involve terms that have been divided by other terms. As with all equations, using , or doing the opposite, keeps the equation balanced.

Example 1

Solve the equation \(\frac{3s + 9}{4} = 7\).

This means \(3s + 9\) has all been divided by 4. To solve the equation, inverse the operations. The opposite of dividing by 4 is multiplying by 4. Any operation must be applied to both sides of the equation, so multiply both sides by 4.

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On the left hand side, the division by 4 and the multiplication by 4 cancel each other out
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The inverse of adding 9 is subtracting 9. Subtract 9 from each side
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3s means 3 × s. The inverse of multiplying by 3 is dividing by 3. Divide both sides by 3

Example 2

Solve the equation \(9 - m = \frac{8m + 5}{3}\).

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8m + 5 has been divided by 3. The opposite of dividing by 3 is multiplying by 3, so multiply each side by 3
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Remember to multiply the entire left-hand side by 3
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Expand the bracket. When letters are on both sides, move the smallest letter, this is -3m. Add 3m to each side
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The opposite of adding 5 is subtracting 5. Subtract 5 from each side
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11m means 11 × m, so inverse this step to isolate m. Divide both sides by 11