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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.

'Solve Simple Linear Equations with Unknown on Each Side' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Solve Linear Equations (One Variable)

Difficulty level:  

down

Worksheet Overview

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

 

Check answer

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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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

CORRECT ANSWER
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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