"I think of a number, subtract 6 then multiply by 7 and the answer is 63. What number am I thinking of?"
If you have completed 'Two-step Equations' you will be familiar with this sort of puzzle. In fact, you may be thinking this is the same, but there is an important difference in the order of operations. In this puzzle, the subtraction is performed before the multiplication and this makes a difference when we write it as an equation. Normally, in mathematics multiplication and division are performed before addition and subtraction. if we want to change this order we need to use brackets. So in order to write this puzzle as an equation with x as the unknown number we write:
7(x - 6) = 63
The x - 6 is in the bracket as this was the first step. The 7 outside the bracket means 'times 7' and was the second step. This type of equation can still be solved using the 'balancing' method where we always 'do the same to both sides' to get the x by itself. Since the x7 was performed last we 'undo' this first by ÷7, then we undo the -6 by +6.
We set out our working as follows:
So the number I thought of was 15.
Here is another equation, a little more complicated.
3(2x + 9) = 51
We need to think carefully about this one. First, the x is multiplied by 2 (2x) then 9 is added (2x + 9) and finally, it is multiplied by 3. So we need to use the inverses of these in the reverse order. Here is our working.
Now, technically this is a 3-step equation, but it uses the same method as the 2-step ones, there's just an extra line of working.
You should be getting pretty familiar with solving equations by now so no more examples. Are you ready to try some?