 # 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. Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Equations and Algebra

Difficulty level:   ### 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 = ________

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 = ________

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 = ________

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 = ________

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 = ________

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 = ________

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 = ________

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 = ________

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 = ________

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 = ________

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 ----

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