# Solve Simple Linear Equations with Unknown on Each Side

In this worksheet, students practise to solve simple linear equations where there are unknowns on each side.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Solve Linear Equations (One Variable)

Difficulty level:

### QUESTION 1 of 10

Follow this example and the steps used to solve this simple equation with unknowns on both sides.

Example

3x - 4 = 5x - 20

Method

Reverse so that the bigger x term is on the left (this move is optional but makes it easier)

5x - 20 = 3x - 4

Subtract 3x from both sides

2x - 20 = -4

Add 20 to both sides

2x = 16

Divide both sides by 2

x = 8

Substitute x = 8 into the original equation 3x - 4 = 5x - 20

Left hand side = 3 x 8 - 4 = 24 - 4 = 20

Right hand side = 5 x 8 - 20 = 40 - 20 = 20

Solve

x + 10 = 3x + 5

x = 2½

x = 3

Solve

3x - 9 = 4x + 6

x = -17

x = -15

Solve

2x + 10 = x - 9

x = -17

x = -19

Solve

x - 6 = 3x - 12

x = 3

x = 4

Solve

3x + 9 = 4x + 10

x = 19

x = -1

Solve

3x - 11 = 5x + 9

x = -1

x = -10

Solve

5x + 8 = x - 8

x = -4

x = 0

Solve

5x - 3 = 2x - 12

x = -5

x = -3

Solve

2x + 8 = 3x - 5

x = 13

x = -13

Solve

2x + 5 = 4x - 9

x = 7

x = -2

• Question 1

Solve

x + 10 = 3x + 5

x = 2½
EDDIE SAYS

Reverse the equation so the larger unknown is on the left

3x + 5 = x + 10

Subtract x from both sides

3x + 5 - x = x + 10 - x

2x + 5 = 10

Subtract 5 from both sides

2x + 5 - 5 = 10 - 5

2x = 5

x = 2.5

• Question 2

Solve

3x - 9 = 4x + 6

x = -15
EDDIE SAYS

Reverse the equation so the larger unknown is on the left

4x + 6 = 3x - 9

Subtract 3x from both sides

4x + 6 - 3x = 3x - 9 - 3x

x + 6 = -9

Subtract 6 from both sides

x + 6 - 6 = =9 - 6

x = -15

• Question 3

Solve

2x + 10 = x - 9

x = -19
EDDIE SAYS

Subtract x from both sides

2x + 10 - x = x - 9 - x

x + 10 = - 9

Subtract 10 from both sides

x + 10 - 10 = -9 - 10

x = -19

• Question 4

Solve

x - 6 = 3x - 12

x = 3
EDDIE SAYS

Reverse the equation so the larger unknown is on the left

3x - 12 = x - 6

Subtract x from both sides

3x - 12 - x = x - 6 - x

2x - 12 = - 6

Add 12 to both sides

2x -12 + 12 = -6 + 12

2x = 6

x = 3

• Question 5

Solve

3x + 9 = 4x + 10

x = -1
EDDIE SAYS

Reverse the equation so the larger unknown is on the left

4x + 10 = 3x + 9

Subtract 3x from both sides

4x + 10 - 3x = 3x + 9 - 3x

x + 10 = 9

Subtract 10 from both sides

x + 10 - 10 = 9 - 10

x = -1

• Question 6

Solve

3x - 11 = 5x + 9

x = -10
EDDIE SAYS

Reverse the equation so the larger unknown is on the left

5x + 9 = 3x - 11

Subtract 3x from both sides

5x + 9 - 3x = 3x - 11 - 3x

2x + 9 = -11

Subtract 9 from both sides

2x + 9 - 9 = -11 - 9

2x = -20

x = - 10

• Question 7

Solve

5x + 8 = x - 8

x = -4
EDDIE SAYS

Subtract x from both sides

5x + 8 - x = x - 8 - x

4x + 8 = -8

Subtract 8 from both sides

4x + 8 - 8 = -8 - 8

4x = -16

x = -4

• Question 8

Solve

5x - 3 = 2x - 12

x = -3
EDDIE SAYS

Subtract 2x from both sides

5x -3 - 2x = 2x - 12 - 2x

3x - 3 = -12

Add 3 to both sides

3x - 3 + 3 = -12 + 3

3x = -9

x = -3

• Question 9

Solve

2x + 8 = 3x - 5

x = 13
EDDIE SAYS

Reverse the equation so the larger unknown is on the left

3x - 5 = 2x + 8

Subtract 2x from both side

3x - 5 - 2x = 2x + 8 - 2x

x - 5 = 8

Add 5 to both sides

x - 5 + 5 = 8 + 5

x = 13

• Question 10

Solve

2x + 5 = 4x - 9

x = 7
EDDIE SAYS

Reverse the equation so the larger unknown is on the left

4x - 9 = 2x + 5

Subtract 2x from both sides

4x - 9 - 2x = 2x + 5 - 2x

2x - 9 = 5

Add 9 to both sides

2x - 9 + 9 = 5 + 9

2x = 14

x = 7

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