Solving equations
Solving an equation means finding the value or values for which the two expressions on each side of the equals sign are equal. One of the most common methods used to solve equations is the balance method.
Imagine an equation as a set of scales. The scales will stay in balance as long as the same operation (addition, subtraction, multiplication or division) is applied to both sides.
Example
Solve the equation \(3a + 8 = 26\).
The equation can be shown in balance on a set of scales.
The value of \(a\) must be found that balances \(3a + 8\) with 26.
The term \(+8\) can be removed from the equation by subtracting 8 from each side. This gives \(3a + 8 - 8 = 26 - 8\).
This simplifies to \(3a = 18\). \(3a\) means \(3 \times a\), so to get \(a\) by itself, divide both sides by 3. This gives \(3a \div 3 = 18 \div 3\).
This simplifies to \(a = 6\).
This answer can be checked by substituting \(a = 6\) back into the original equation \(3a + 8 = 26\).
Substitute \(a = 6\):
\(3a + 8 = 3 \times 6 + 8 = 18 + 8 = 26\)
The equation balances, so \(a = 6\) is the correct answer.
Question
Solve the equation \(4y + 5 = -3\).
Start by isolating \(4y\) on the left hand side of the equation by subtracting 5 from each side. This will remove the term \(+5\).
\(4y + 5 = -3\)
Subtract 5 from each side:
\(4y + 5 - 5 = -3 - 5\)
Simplify:
\(4y = -8\)
Get \(y\) by itself by dividing both sides by 4:
\(4y \div 4 = -8 \div 4\)
\(y = -2\)
This answer can be checked by substituting \(y = -2\) into the original equation.
\(4y + 5 = 4 \times -2 + 5 = -8 + 5 = -3\)
The equation balances, so \(y = -2\) is the final answer.