# Solve Inequalities

In this worksheet, students practise solving inequalities.

Key stage:  KS 3

Curriculum topic:   Algebra

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

Difficulty level:

### QUESTION 1 of 10

This worksheet is about solving inequalities.

Inequalities will give you a range of answers for you unknown which could be greater than (>), greater than or equal to (≥), less than (<), less than or equal to (≤).

They are solved in the same way as equations, either by working backwards doing inverses, or carrying out the same operation to each side.

Just one operation needs care - multiplying or dividing each side by a negative number will reverse the inequality sign.

This can be illustrated as follows:

We know that 10 > 4

Multiplying each side by -2 gives -20 > -8 .

This is obviously NOT TRUE

Reversing the sign makes it correct -20 < -8 .

Solve the inequality:

9x + 10 > 73

x > 7

x > 4

x > 8

x > 6

Solve the inequality:

7x + 11 ≥ 39

x > 7

x ≥ 4

x ≤ 4

x > 6

Solve the inequality:

2x + 6 > 22

x > 7

x > 4

x > 8

x = 8

Solve the inequality:

-7x + 2 ≤ 44

x > 7

x < 6

x ≤ -6

x ≥ -6

Solve the inequality:

4x + 7 > 19

x > 3

x > 1

x > 4

x > 5

Solve the inequality:

5x + 7 < 12

x > 3

x < 1

x > 4

x < 5

Solve the inequality:

5x + 4 < 24

x < 3

x < 1

x < 4

x < 5

Solve the inequality:

4x + 6 > 26

x > 3

x = 1

x < 4

x > 5

Solve the inequality:

6x + 4 ≤ -20

x < 3

x ≥ 4

x ≤ -4

x < -4

Solve inequalities:

3 - 3x > 9

x > -2

x > 2

x < -2

x < 2

• Question 1

Solve the inequality:

9x + 10 > 73

x > 7
EDDIE SAYS

Subtract 10 from both sides

9x + 10 - 10 > 73 - 10

9x > 63

Divide through by x

9x ÷ 9 > 63 ÷ 9

x > 7

• Question 2

Solve the inequality:

7x + 11 ≥ 39

x ≥ 4
EDDIE SAYS

Subtract 11 from both sides

7x + 11 - 11 > 39 - 11

7x ≥ 28

Divide through by x

7x ÷ 7 ≥ 28 ÷ 7

x ≥ 7

• Question 3

Solve the inequality:

2x + 6 > 22

x > 8
EDDIE SAYS

Subtract 6 from both sides

2x + 6 - 6 > 22 - 6

2x > 16

Divide through by 2

2x ÷ 2 > 16 ÷ 2

x > 8

• Question 4

Solve the inequality:

-7x + 2 ≤ 44

x ≥ -6
EDDIE SAYS

Subtract 2 from both sides

-7x + 2 - 2 ≤ 44 - 2

-7x ≤ 42

Divide through by -7

-7x ÷ -7 ≤ 42 ÷ -7

x ≥ -6

Remember that dividing through by a negative will switch the sign.

• Question 5

Solve the inequality:

4x + 7 > 19

x > 3
EDDIE SAYS

Subtract 7 from both sides

4x + 7 - 7 > 19 - 7

4x > 12

Divide through by 4

4x ÷ 4 > 12 ÷ 4

x > 3

• Question 6

Solve the inequality:

5x + 7 < 12

x < 1
EDDIE SAYS

Subtract 7 from both sides

5x + 5 - 7 < 12 - 7

5x < 5

Divide through by 5

5x ÷ 5 < 5 ÷ 5

x < 1

• Question 7

Solve the inequality:

5x + 4 < 24

x < 4
EDDIE SAYS

Subtract 4 from both sides

5x + 4 - 4 < 24 - 4

5x < 20

Divide through by 5

5x ÷ 5 < 20 ÷ 5

x < 4

• Question 8

Solve the inequality:

4x + 6 > 26

x > 5
EDDIE SAYS

Subtract 6 from both sides

4x + 6 - 6 > 26 - 6

4x > 20

Divide through by 4

4x ÷ 4 > 20 ÷ 4

x > 5

• Question 9

Solve the inequality:

6x + 4 ≤ -20

x ≤ -4
EDDIE SAYS

Subtract 4 from both sides

6x + 4 - 4 ≤ -20 - 4

6x ≤ -24

Divide through by 6

6x ÷ 6 ≤  -24 ÷ 6

x ≤ -4

• Question 10

Solve inequalities:

3 - 3x > 9

x < -2
EDDIE SAYS

Subtract 3 from both sides

3 - 3x - 3 > 9 - 3

-3x > 6

Divide through by -3

-3x ÷ -3 > 6 ÷ -3

x < -2

Remember that if you divide by a negative number, you must switch the inequality around

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