1. Solving Linear Equations
Which level would you like to study?
Level 5
Level 6
Level 7
Worksheet

2. Level 5
Objective: Be able to solve linear equations with an unknown on one side.

3. 4a = 24 a = 24 4 = 6 Low level 5 This means “4 multiplied by a”
What is the inverse operation?
= 6
Division

4. b = 3 5 b = 3 x 5 = 15 Low Level 5 This means “b divided by 5”
What is the inverse operation?
= 15
Multiplication

5. 3a + 8 = 35 3a = 35 - 8 3a = 27 a = 27 3 = 9 High Level 5
Let’s make this question into a low level 5 question. We know how to solve those!
3a =
This is the only bit that is different. We can use inverse operations to get rid of it.
This says “add 8”
3a = 27
What is the inverse operation?
a = 27 3
Subtract
Look! A low level 5 question!
= 9

6. Level 6
Objective: Be able to solve linear equations with an unknown both sides.

7. 5a + 3 = 2a + 12 5a = 2a + 12 - 3 5a = 2a + 9 5a – 2a = 9 3a = 9 a = 9
Low level 6
5a + 3 = 2a + 12
Let’s start by removing this.
5a = 2a
5a = 2a + 9
Doing this removes the add 3, but remember to subtract 3 from the other side too!
5a – 2a = 9
This says add 3
Now, let’s remove this.
3a = 9
To “get rid of” our 2a, we have to subtract 2a
What is the inverse operation?
a = 9
A 3
= 3
Subtract 3

8. 5(a - 4) = 3(a + 2) 5a - 20 = 3a + 6 5a = 3a + 6 + 20 5a = 3a + 26
Expanding Brackets Tutorial
High Level 6
5(a - 4) = 3(a + 2)
5a - 20 = 3a + 6
5a = 3a
First expand the brackets (Click the tutorial button above if you cannot remember how to do this)
Now we have a low level 6 question which can be solved just as before.
5a = 3a + 26
5a – 3a = 26
2a = 26
a = 13

9. Level 7
Objective: Be able to solve linear equations with an unknown on one side, including problems where the coefficients are fractional

10. Level 7