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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 'by itself' on the left hand side, with our answer on the right. Our first step is to 'undo' the 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 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 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. 

Kathryn P. GCSE Maths tutor, A Level English tutor, GCSE English tuto...

10 months ago

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