The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Solve Equations (of the form ax + b = c) Using the Inverse Method

In this worksheet, students will solve equations of the form ax + b = cusing the inverse method.

'Solve Equations (of the form ax + b = c) Using the Inverse Method' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

In this worksheet, we will learn how to solve equations by using the inverse method.

Letters are used to represent numbers in algebra.

In an equation, one letter represents just one value.

 

Example

3x + 4 = 13.

Here, we have started with the unknown value x, multiplied it by 3 and added 4 to get the result 13.

 

Method

To find out what the unknown value is, we must "unravel" the equation by working backwards, using inverses.

We always deal with the thing that is not with the 'x', so to get rid of the + 4 we subtract the 4 from both sides

3x + 4 - 4 = 13 - 4

3x = 9

Now, divide both sides by 3 so that we have the x by itself.

3x ÷ 3 = 9 ÷ 3

x = 3

The answer x = 3 will work if you substitute it back into the equation.
3 × 3 + 4 = 13.

9 + 4 = 13

13 = 13

So x = 3 is the correct answer!

Solve the equation:

6x - 7 = 23

 

x = ________

 

 

Solve the equation:

3x + 5 = 26

 

x = ________

Solve the equation:

8x + 9 = 57

 

x = ________

Solve the equation:

5x - 4 = 1

 

x = ________

Solve the equation:

8x + 9 = 25

 

x = ________

Solve the equation:

9x - 5 = 4

 

x = ________

Solve the equation:

9x + 12 = 39

 

x = ________

Solve the equation:

5x + 8 = 43

 

x = ________

 

Solve the equation:

9x - 9 = 54

 

x = ________

Solve the equation:

4x - 7 = 17

 

x = ________

  • Question 1

Solve the equation:

6x - 7 = 23

 

x = ________

 

 

CORRECT ANSWER
5
EDDIE SAYS

We have a multiply by 6 with the x and a minus 7.

To get rid of these;

We first add 7 (because it's the opposite of - 7 and it isn't with the x

Then we divide by 6 because it is the opposite of multiply by 6

6x - 7 + 7 = 23 + 7

6x = 30

6x ÷ 6 = 30 ÷ 6

x = 5

  • Question 2

Solve the equation:

3x + 5 = 26

 

x = ________

CORRECT ANSWER
7
EDDIE SAYS

We have a multiply by 3 with the x and a plus 5.

To get rid of these;

We first subtract 5 (because it's the opposite of + 5 and it isn't with the x

Then we divide by 3 because it is the opposite of multiply by 3

3x + 5 - 5 = 26 - 5

3x = 21

3x ÷ 3 = 21 ÷ 3

x = 7

  • Question 3

Solve the equation:

8x + 9 = 57

 

x = ________

CORRECT ANSWER
6
EDDIE SAYS

We have a multiply by 8 with the x and a plus 9.

To get rid of these;

We first subtract 9 (because it's the opposite of + 9 and it isn't with the x

Then we divide by 8 because it is the opposite of multiply by 8

8x + 9 - 9 = 57 - 9

8x = 48

8x ÷ 8 = 48 ÷ 8

x = 6

  • Question 4

Solve the equation:

5x - 4 = 1

 

x = ________

CORRECT ANSWER
1
EDDIE SAYS

We have a multiply by 5 with the x and a minus 4.

To get rid of these;

We first add 4 (because it's the opposite of - 4 and it isn't with the x

Then we divide by 5 because it is the opposite of multiply by 5

5x - 4 + 4 = 1 + 4

5x = 5

5x ÷ 5 = 5 ÷ 5

x = 1

  • Question 5

Solve the equation:

8x + 9 = 25

 

x = ________

CORRECT ANSWER
2
EDDIE SAYS

We have a multiply by 8 with the x and a plus 9.

To get rid of these;

We first subtract 9 (because it's the opposite of + 9 and it isn't with the x

Then we divide by 8 because it is the opposite of multiply by 8

8x + 9 - 9 = 25 - 9

8x = 16

8x ÷ 8 = 16 ÷ 8

x = 2

  • Question 6

Solve the equation:

9x - 5 = 4

 

x = ________

CORRECT ANSWER
1
EDDIE SAYS

We have a multiply by 9 with the x and a minus 5.

To get rid of these;

We first add 5 (because it's the opposite of - 5 and it isn't with the x

Then we divide by 9 because it is the opposite of multiply by 9

9x -5 + 5 = 4 + 5

9x = 9

9x ÷ 9 = 9 ÷ 9

x = 1

  • Question 7

Solve the equation:

9x + 12 = 39

 

x = ________

CORRECT ANSWER
3
EDDIE SAYS

We have a multiply by 9 with the x and a plus 12.

To get rid of these;

We first subtract 12 (because it's the opposite of + 12 and it isn't with the x

Then we divide by 9 because it is the opposite of multiply by 9

9x + 12 - 12 = 39 - 12

9x = 27

9x ÷ 9 = 27 ÷ 9

x = 3

  • Question 8

Solve the equation:

5x + 8 = 43

 

x = ________

 

CORRECT ANSWER
7
EDDIE SAYS

We have a multiply by 5 with the x and a plus 8.

To get rid of these;

We first subtract 8 (because it's the opposite of + 8 and it isn't with the x

Then we divide by 5 because it is the opposite of multiply by 5

5x + 8 - 8 = 43 - 8

5x = 35

5x ÷ 5 = 35 ÷ 5

x = 7

  • Question 9

Solve the equation:

9x - 9 = 54

 

x = ________

CORRECT ANSWER
7
EDDIE SAYS

We have a multiply by 9 with the x and a minus 9.

To get rid of these;

We first add 9 (because it's the opposite of - 9 and it isn't with the x

Then we divide by 9 because it is the opposite of multiply by 9

9x - 9 + 9 = 54 + 9

9x = 63

9x ÷ 9 = 63 ÷ 9

x = 7

  • Question 10

Solve the equation:

4x - 7 = 17

 

x = ________

CORRECT ANSWER
6
EDDIE SAYS

We have a multiply by 4 with the x and a minus 7.

To get rid of these;

We first add 7 (because it's the opposite of - 7 and it isn't with the x

Then we divide by 4 because it is the opposite of multiply by 4

4x - 7 + 7 = 17 + 7

4x = 24

4x ÷ 7 = 24 ÷ 4

x =  6

---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1