Solving equations with fractions
Some equations involve terms that have been divided by other terms. As with all equations, using Inverse operations are opposite calculations often used in solving equations. To remove +9 from a sum, perform the inverse operation which is -9., 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.
Image caption, On the left hand side, the division by 4 and the multiplication by 4 cancel each other out
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Example 2
Solve the equation \(9 - m = \frac{8m + 5}{3}\).
Image caption, 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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Check this answer by substituting \(m = 2\) into the original equation.
\(9 - m = \frac{8m + 5}{3}\)
\(9 - 2 = \frac{8 \times 2 + 5}{3}\)
\(7 = \frac{16 + 5}{3}\)
\(7 = \frac{21}{3}\)
\(7 = 7\)
The equation balances, so this is the correct solution.