The function machine approach is a good method. But it won’t solve all equations. Sometimes we have equations with unknowns (represented by letters) on both sides of the equation. In this case we can treat the equation like a balance scale to solve it. Whatever we do to one side of the scale, we must also do to the other side.

Let’s use this approach to consider solving the equation 2x = x+5

In general, our aim when solving an equation is to get the “letter” on its own. But anything we do to one side of the equation we must also do to the other side of the equation.

Examples

Exercise

Let’s complete questions 2 to 5 from exercise 8C on page 119 of the textbook:

The answers are below:

Expanding brackets before solving

Sometimes when there are brackets in equations we will need to expand the brackets before solving the equation:

Example

Exercise

Let’s complete exercise 8D on page 120 of the textbook:

The answers are below: