Solve 8(x + 3) = 36

In this question (taken from a non-calculator higher level GCSE maths past paper), we want to find an answer x=?

Ultimately we want to leave x 'by itself' on the left hand side, with our answer on the right. Our first step is to 'undo' the 8 on the outside of the bracket. This is done by dividing by 8 on both sides of the equation.  After dividing by 8 we have (x+3)=(36/8).

Because this is a non-calculator paper, you may find it easiest to calculate 36/8 in stages. We can see very easily that both 36 and 8 are both divisible by 2. This allows us to simplify the fraction to 18/4. Repeating this step again gives a simplified fraction 9/2. It is now easier to see that 36/8=9/2=4.5 and so x+3=4.5. 

Finally we 'undo' the 3 on the left hand side of the equation by subtracting 3 on both sides of the equation. This gives us x=4.5-3 so x=1.5. This is the final answer. 

It is worth noting that although we have gone through the stages step-by-step in this example, the question is only worth 3 marks in the exam. You should practice these types of algebra-solving questions such that you are able to solve them whilst presenting your workings clearly, quite quickly.