When we are using this strategy, we need to make sure that we have all of the unknowns on one side of the equation and all of the numbers on the other side of the equation. All the examples that we look at in this section will be like this, but in the next section, we will need to modify the equation so that this is the case.

**Example 1**

Solve the equation below.

*y*is; instead we want to know what

*y*is. Therefore, we divide both sides of the equation by 4.

*y*is 5. Like before, we can check that our answer is correct by subbing

*y*as 5 back into the equation.

*y*is correct;

*y*is 5.

**Example 2**

Find the value of

*a*.

*a*is 18. We want to find the value of

*a*and not 6

*a*. Therefore, we divide both sides of the equation by 6.

*a*is equal to 3. We can check that

*a*is 3 by subbing

*a*as 3 into the original equation. The working is shown below.

*a*is 3.

**Example 3**

Find the value for

*z*in the equation below.

- One method is to divide both sides of the equation by the coefficient of the unknown.
- The other method is to multiply both sides of the equation by the denominator of the coefficient of the unknown. The whole point of doing this is to get rid of the fraction for the unknown. We then divide both sides of the equation by what was the numerator of the coefficient of the unknown if the numerator of the coefficient is not 1. This method is easier to use when we are unable to use a calculator.

**Method 1**

Let’s use the first method; dividing both sides by the coefficient of the unknown. The coefficient of z is ½, thus meaning that we divide both sides of the equation by ½.

*z*.

**Method 2**

The other method is to multiply both sides by the denominator of the coefficient of the unknown, and then divide both sides by what was the numerator of the coefficient of the unknown (if the numerator is not 1). The coefficient of the unknown is ½. The denominator of the coefficient is 2. Therefore, we multiply both sides of the equation by 2.

This means that z is 14, which is exactly the same answer that we found using the other method.

**Example 4**

Find the value of

*r*.

Like the question before, there are two methods to obtain the value of r.

**Method 1**

The first method is to divide both sides by the coefficient of the unknown, which means that we are dividing by ^{3}/_{2} (1.5).

For the above question, it was not too hard dividing by ^{3}/_{2}, but you may sometimes be given a fraction that is much harder, which means that you may find the next method easier.

**Method 2**

In the next method, we multiply both sides of the equation by the denominator of the coefficient of the unknowns. We then divide both sides by what was the numerator of the coefficient of the unknowns providing that the numerator is not 1. The coefficient of the unknowns is ^{3}/_{2} and the denominator is 2. Therefore, we multiply both sides by 2.