Solve: 1. |x – 4| = 9

2.|7x – 2| = 5

3.|3x – 2| + 4 = 21

Write the inequality shown:

4.

5.-3 20

4-4 0

3{1, }

7

19{ , 5}

3

{13, 5}

3 or 2x x

4 4x

WU 36

9.4 Inequalities and Absolute Value

Goal(s): Solve and graph inequalities involving absolute value in the form of

A > b and A < b

2 Cases

• [A] <b (less than)

• Conjunction

• -b<A<b

• [A] >b (greater than)

• Disjunction

• A<-b or A>b

Solve and graph:|x + 2| 5

x + 2 = 5

x = 3

x + 2 = -5

x = -7

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

To solve an inequality of the form |A| < b, where b is a positive number, we solve the conjunction –b < A < b.

Solve and graph:|4x - 10| > 2

4x - 10 = 2

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

1. Solve for both end points.

2. Write solution as disjunction (x< 2 or x > 6)

2104 xx = 3 4 8x

2 or 3x x

Solve and graph:|3x - 8| 5

3x - 8 = 5

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

To solve an inequality of the form |A| > b, where b is a positive number, we solve the disjunction A < -b or A > b.

583 x3x = 13 33 x

1x3

13x

3

13xor 1 x

Solve and graph:|3x| 18

x = 6 x = -6

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

-6 x 6

To solve an inequality of the form |A| < b, where b is a positive number, we solve the conjunction –b < A < b.

Solve and graph: |3x – 4 | 2

x = 2

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

2/3 x 2

3 4 2x 3 4 2x 3 6x 3 2x 2

3x

Solve and graph: |4x – 9 | 7

x = 4

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

4 9 7x 4 9 7x 4 16x 4 2x 1

2x

14

2x

Solve and graph: |3x +4 | 19

x = 5

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

3 4 19x 3 4 19x 3 15x 3 23x 23

3x

27

3x

235

2x

Solve and graph: |7x + 4 |+ 6 2

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

6 6

7 4 4x

Solve :

8 or 7x x

2 15

3

x

2 15

3

x

2 15

3

x

2 1 15x 2 1 15x

2 14x 7x

2 16x 8x

Assignment:

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