� Solve inequalities that contain more than one operation

Inequalities that contain more than one operation require more than one step to solve. Use inverse operations to undo the operations in the inequality one at a time.

Step 1: Undo addition or subtraction

Step 2: Undo multiplication and division

Is your variable isolated?

Solving Multi-Step Inequalities

Solve the inequality and graph the solutions.

45 + 2b > 61 45 + 2b > 61

–45 –45 2b > 16

b > 8

0 2 4 6 8 10 12 14 16 18 20

1. Add/ Subtract

2. Multiply/Divide

The solution set is {b:b > 8}.

8 – 3y ≥ 29 8 – 3y ≥ 29

–8 –8

–3y ≥ 21

y ≤ –7

1. Add/Subtract

2. Multiply/Divide

–10 –8 –6 –4 –2 0 2 4 6 8 10

–7

Solving Multi-Step Inequalities

Solve the inequality and graph the solutions.

The solution set is {y:y d –7}.

Simplifying Before Solving Inequalities Solve the inequality and graph the solutions.

–4(2 – x) ≤ 8

–10 –8 –6 –4 –2 0 2 4 6 8 10

Name: _____________________________

Solving Two-Step Inequalities – (Lesson 4.4)

x You can solve two-step _________________________ in the same way you solve two-step equations.

Solving Two-Step Inequalities:

Solve.

5x – 4 ≥ 11 3�b + 4 < 13 19 ≤ 4 – 3d

6y – 7 > 5 9 < 4�w + 8 -17 ≤ 3y – 4

Graphing an Inequality:

Solve and Graph.

-7(x + 3) ≤ 28 -3 ≤ 0.5( 8 + y)

Real-Life Application:

A contestant in a weight-loss competition wants to lose an average of at least 8 pounds per month during a 5-month period. How many pounds must the constant lose in the fifth month to meet the goal?

Progress Report

Month Pound Lost

1 12 2 9 3 5 4 8

Name : Score :

Printable Math Worksheets @ www.mathworksheets4kids.com

Solve each inequality.

2x + 5 > 131) 2) 5x – 7 ≥ 83)

4) 9x – 3 > 65) 11 + 3x ≤ 176)

8) 9)4x – 12 ≥ 87)

10) 7x – 3 > 1811) 12)

3x + 7 < 9

3x + 1 ≥ 7

x – 43

≤ 5

x4

+1 > 10

x – 64

≤ 2

x2

+ 4 < 7

Solving Two-Step Inequalities ES1

Name : Score :

Printable Math Worksheets @ www.mathworksheets4kids.com

Solve each inequality.

2x + 5 > 131) 2) 5x – 7 ≥ 83)

4) 9x – 3 > 65) 11 + 3x ≤ 176)

8) 9)4x – 12 ≥ 87)

10) 7x – 3 > 1811) 12)

3x + 7 < 9

3x + 1 ≥ 7

x – 43

≤ 5

x > 4

x ≥ 5

x ≤ 14

x < 6

x ≥ 3

x > 36

x ≥ 2

x ≤ 2

x4

+1 > 10

x > 1

x > 3

x ≤ 19

x < 23

x – 64

≤ 2

x2

+ 4 < 7

Solving Two-Step Inequalities

Answer key

ES1

Name : Score :

Printable Math Worksheets @ www.mathworksheets4kids.com

Solve each inequality and graph the solution.

3) 7x – 19 < 16

2) 4x + 5 ≤ 13

8) 2x + 5 ≥ 19

2 4 60-2-4 8

5) 9 + 3x > 12 6) 3x – 4 ≤ 5

4)

7)

0 10 20-10-20-30 30 7 14 210-7-14 28

3 5 7-1-3 9

1)

x – 45

≥ 2

x8

+ 1 < 3

-1 0 1 2 3 4-2-3-4-5-6 5 6

5 15-15-25 25-5

0 2 4 61 8-2 1 3 5 7-1-3

0 8 16-8-16-24 24 -7 0 7 14 21 28-14-21-28-35-42 35 42

x2

+ 3 > 9

-2 0 2 4 6 8-4 10 12 14 16 18 20

Solving & Graphing Inequalities ES1

Name : Score :

Printable Math Worksheets @ www.mathworksheets4kids.com

Solve each inequality and graph the solution.

3) 7x – 19 < 16

x > 12 x ≤ 2

x < 5

2) 4x + 5 ≤ 13

x ≥ 14

x > 1

8) 2x + 5 ≥ 19

x ≤ 3

2 4 60-2-4 8

5) 9 + 3x > 12

x < 16

6) 3x – 4 ≤ 5

x ≥ 7

4)

7)

0 10 20-10-20-30 30 7 14 210-7-14 28

3 5 7-1-3 9

1)

x – 45

≥ 2

x8

+ 1 < 3

-1 0 1 2 3 4-2-3-4-5-6 5 6

5 15-15-25 25-5

0 2 4 61 8-2 1 3 5 7-1-3

0 8 16-8-16-24 24 -7 0 7 14 21 28-14-21-28-35-42 35 42

x2

+ 3 > 9

-2 0 2 4 6 8-4 10 12 14 16 18 20

Solving & Graphing Inequalities

Answer key

ES1

Name :Teacher : Date :

Score :

Math-Aids.Com

Solve and Graph the InequalitiesSolve and Graph the Inequalities

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Name :Teacher : Date :

Score :

Math-Aids.Com

Solve and Graph the InequalitiesSolve and Graph the Inequalities

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