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5.4 – Solving Compound Inequalities

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5.4 – Solving Compound Inequalities

Ex. Solve and graph the solution.

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4

-1 < x

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

0

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

-1

0

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

-1

0

6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 <x < 6

-1

0

6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 <x < 6

-1

0

6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x< 6

-1

0

6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x< 6

-1

0

6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

-1

0

6

Ex. Solve and graph the solution.

a. -5 < x – 4 < 2

-5 < x – 4 and x – 4 < 2

+4 +4 +4 +4

-1 < x and x < 6

-1 < x < 6

-1

0

6

b. -3h + 4 < 19 or 7h – 3 > 18

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4

-3h < 15

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4

-3h < 15

-3 -3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4

-3h < 15

-3 -3

h > -5

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15

-3 -3

h > -5

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3

h > -5

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

0

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h> -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h> 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h> -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h> 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h> -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

c. 1 + x< -3 or -x< -4

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

c. 1 + x< -3 or -x< -4

-1 -1

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

c. 1 + x< -3 or -x< -4

-1 -1

x< -4 or x> 4

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

c. 1 + x< -3 or -x< -4

-1 -1

x< -4 or x> 4

-5

0

3

b. -3h + 4 < 19 or 7h – 3 > 18

- 4 - 4 +3 +3

-3h < 15 or 7h > 21

-3 -3 7 7

h > -5 or h > 3

c. 1 + x< -3 or -x< -4

-1 -1

x< -4 or x> 4

-5

0

3

-4

0

4