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.

3a + 8 = 26

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 \frac{3a}{3} = \frac{18}{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.