We’ve seen how to solve equations by doing one thing to both sides of an equation. Below are two examples:
Problem | Solution |
n + 17 = 100 | |
Take 17 away from both sides to leave a on the left | n + 17 – 17 = 100 – 17 n + 0 = 83 n = 83 |
Problem | Solution |
6y = 54 | |
Divide both sides by 6 | 6y ÷ 6 = 54 ÷ 6 y = 9 |
Sometimes there are problems that need slightly more complicated equations. For example, let’s say you want to buy a coat that costs $100. You have $40. Your mum has told you that she will match whatever amount of money you can save to help you buy the coat. How much do you need to save?
Amount you need to save | let’s call it ‘n’ |
Amount you’ll have after you have saved and your mum has matched (or doubled) it. |
2 x n (or 2n) |
Amount you already have | 40 |
Amount you need | 100 |
Putting it altogether | 2n + 40 = 100 |
To solve equations like 2n + 40 = 100 we need to “get rid of” two things: the +40 and the x2. We need to do two things and the order we do them in is important. The examples below show what we can do to solve these types of equations:
2n + 40 = 100 | |
Step 1: Subtract 40 from both sides | 2n + 40 – 40 = 100 – 40 |
2n = 60 | |
Step 2: Divide both sides by 2 | 2n ÷ 2 = 60 ÷ 2 |
n = 30 |
It is very important that we solve equations like the ones on this page by doing the addition or subtraction before doing the division or multiplication.
3n – 7 = 17 | |
Step 1: Add 7 to both sides | 3n – 7 + 7 = 17 + 7 |
3n = 24 | |
Step 2: Divide both sides by 3 | 3n ÷ 3 = 24 ÷ 3 |
n = 8 |
^{a}/_{7} + 8 = 9 | |
Step 1: Subtract 8 from both sides | ^{a}/_{7} + 8 – 8 = 9 – 8 |
^{a}/_{7} = 1 | |
Step 2: Multiply both sides by 7 | ^{a}/_{7} x 7 = 1 x 7 |
a = 7 |
^{b}/_{2} – 16 = 40 | |
Step 1: Add 16 to both sides | ^{b}/_{2}– 16 + 16 = 40 + 162 |
^{b}/_{2}= 562 | |
Step 2: Multiply both sides by 2 | ^{b}/_{2} x 2 = 56 x 22 |
b = 112 |
Print the worksheets below to help practice solving equations using two steps.
- Solving equations in two steps (1 of 4) e.g. 5n + 4 = 29
- Solving equations in two steps (2 of 4) e.g. a/4 + 3 = 7
- Solving equations in two steps (3 of 4) e.g. 7n – 3 = 18
- Solving equations in two steps (4 of 4) e.g. b/9 – 4 = 6
The four worksheets above are also included here with more solving equations worksheets.