# 10-4 solving multistep inequalities

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8/14/2019 10-4 Solving Multistep Inequalities

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Warm Up

Solve.

1. 6x+ 36 = 2x

2. 4x 13 = 15 + 5x

3. 5(x 3) = 2x+ 3

4. +x=

x= 9

x= 28

x= 6

Course 3

10-4 Solving Multistep Inequalities

78

316 1116x=

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Learn to solvetwo-step inequalities andgraphthe solutions ofan inequalityon a

number line.

Course 3

10-4 Solving Multistep Inequalities

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Solving amultistep inequalityuses the

same inverseoperations as solving amultistepequation. Multiplying ordividing the inequalitybya negative

number reverses the inequalitysymbol.

Course 3

10-4 Solving Multistep Inequalities

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Solve and graph.

Additional Example 1A: Solving Multistep

Inequalities

A. 4x+ 1 > 13

4x+ 1 > 13

1 1 Subtract 1 from both sides.4x > 12

4x4

> 124

Divide both sides by 4.

x> 31 2 3 4 5 6 7

Course 3

10-4 Solving Multistep Inequalities

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Additional Example 1B: Solving Multistep

Inequalities

B. 7 12

5x+ 2 > 12

2 2 Subtract 2 from both sides.5x > 10

5x5

> 105

Divide both sides by 5.

x> 21 2 3 4 5 6 7

Course 3

10-4 Solving Multistep Inequalities

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B. 5

11x

18x+ 8 > 11x 1

8x 8x Subtract 8x from both sides.

8 > 3x 1

93

> 3x3

Add 1 toeach side.

3 >x

-1 0 1 2 3 4 5

+1 +1

9 > 3x

Course 3

10-4 Solving Multistep Inequalities

Divide both sides by 3.

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Solve and graph.

TryThis: Example 2A

A. 15x+30 5x < 10

15x+ 30 5x< 10

30 30 Subtract 30 from both sides.

10x10

< 4010 Divide both sides by 10.

x< 4

-8 -7 -6 -5 -4 -3 -2

10x+ 30 < 10 Combine like terms.

10x < 40

Course 3

10-4 Solving Multistep Inequalities

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TryThis: Example 2B

Multiply byLCD, 20.

12x+ 5 u 10

5 5 Subtract 5 from both sides.

12x u 5

B. + u3x

5

1

4

5

10

+ u3x5

14

510

20( + )u

20( )3x

5

1

4

5

10

20( ) + 20( ) u 20 ( )3x514

510

Course 3

10-4 Solving Multistep Inequalities

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TryThis: Example 2B Continued

xu 5

12

u12x12

512

Divide both sides by 12.

12xu 5

0 5

12

Course 3

10-4 Solving Multistep Inequalities

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TryThis: Example 2C

C. 4x+3 > 8x 1

4x+ 3 > 8x 1

4x 4x Subtract 4x from both sides.

3 > 4x 1

44

> 4x4

Add 1 toeach side.

1 >x

-1 0 1 2 3 4 5

+1 +1

4 > 4x

Course 3

10-4 Solving Multistep Inequalities

Divide both sides by 4.