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 


Step 1: Subtract 8 from both sides 




Step 2: Multiply both sides by 7 


a = 7 


Step 1: Add 16 to both sides 




Step 2: Multiply both sides by 2 


b = 112 
Print the worksheets below to help practice solving equations using two steps.
The four worksheets above are also included here with more solving equations worksheets.