algebra 1b section 5-4

Section 5-4Compound Inequalities

Monday, October 14, 13

Essential Question

✤ How do you solve compound inequalities?

Monday, October 14, 13

Vocabulary

1. Compound Inequality:

2. Intersection:

3. Union:

Monday, October 14, 13

Vocabulary

1. Compound Inequality: Two inequalities that are utilized at the same time

2. Intersection:

3. Union:

Monday, October 14, 13

Vocabulary

1. Compound Inequality: Two inequalities that are utilized at the same time

2. Intersection: A compound inequality the connects the two inequalities using and; Only true if BOTH inequalities are true

3. Union:

Monday, October 14, 13

Vocabulary

1. Compound Inequality: Two inequalities that are utilized at the same time

2. Intersection: A compound inequality the connects the two inequalities using and; Only true if BOTH inequalities are true

3. Union: A compound inequality the connects the two inequalities using or; True if EITHER inequality is true

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11and

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2

and

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2

5 < x

and

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x

and

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and

Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and

1050Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and

1050Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and

1050Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and

1050Monday, October 14, 13

Example 1

a. 7 < x + 2 ≤ 11Solve and graph the solution set.

7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and

{x|5 < x ≤ 9}

1050Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30or

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7

or

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 4k ≤ 32

or

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 4k ≤ 32

or

4 4

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 4k ≤ 32

or

4 4 k ≤ 8

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32

or

4 4 k ≤ 8

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

4 4 k ≤ 8

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

4 4 k ≤ 8

−9 −9

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

4 4 k ≤ 8

−9 −9 k ≤ −2

Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

4 4 k ≤ 8

−9 −9 k ≤ −2

860-2 42Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

4 4 k ≤ 8

−9 −9 k ≤ −2

860-2 42Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

4 4 k ≤ 8

−9 −9 k ≤ −2

860-2 42Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

4 4 k ≤ 8

−9 −9 k ≤ −2

860-2 42Monday, October 14, 13

Example 1

b. 4k − 7 ≤ 25 or 12− 9k ≥ 30Solve and graph the solution set.

4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 −12 −12 4k ≤ 32 −9k ≥ 18

or

{k|k ≤ 8} 4 4 k ≤ 8

−9 −9 k ≤ −2

860-2 42Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5or

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5

or

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −y ≥ 4

or

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −y ≥ 4

or

−1 −1

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −y ≥ 4

or

−1 −1 y ≤ −4

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4

or

−1 −1 y ≤ −4

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

−1 −1 y ≤ −4

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

−1 −1 y ≤ −4

3 3

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

−1 −1 y ≤ −4

3 3 y < −3

Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

−1 −1 y ≤ −4

3 3 y < −3

64-4-6 20Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

−1 −1 y ≤ −4

3 3 y < −3

64-4-6 20Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

−1 −1 y ≤ −4

3 3 y < −3

64-4-6 20Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

−1 −1 y ≤ −4

3 3 y < −3

64-4-6 20Monday, October 14, 13

Example 1

c. − y + 5 ≥ 9 or 3y + 4 < −5Solve and graph the solution set.

−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −4 −4 −y ≥ 4 3y < −9

or

{y|y < −3} −1 −1 y ≤ −4

3 3 y < −3

64-4-6 20Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32and

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

and

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

−12 −12

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

−12 −12 −15 < 5d

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

5 5

−12 −12 −15 < 5d

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

5 5 −3 < d

−12 −12 −15 < 5d

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

5 5 −3 < d

−12 −12 −15 < 5d

d > −3

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12

and

5 5 −3 < d

−12 −12 −15 < 5d

d > −3

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

−12 −12 −15 < 5d

d > −3

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

−12 −12 −15 < 5d

d > −3

−12 −12

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

4 4

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

4 4 d < 5

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

4 4 d < 5

64-4-6 20

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

4 4 d < 5

64-4-6 20

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

4 4 d < 5

64-4-6 20

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

5 5 −3 < d

4 4 d < 5

64-4-6 20

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 1

d. d − 3 < 6d +12 < 2d + 32Solve and graph the solution set.

d − 3 < 6d +12 6d +12 < 2d + 32 −d −d −2d −2d

−3 < 5d +12 4d +12 < 32

and

{d|−3 < d < 5} 5 5 −3 < d

4 4 d < 5

64-4-6 20

−12 −12 −15 < 5d

d > −3

−12 −12 4d < 20

Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per night

Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom

Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

c ≤ 89

Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

c ≤ 89 c ≥ 109

Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

c ≤ 89 c ≥ 109

1101069490 1029886Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

c ≤ 89 c ≥ 109

1101069490 1029886Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

c ≤ 89 c ≥ 109

1101069490 1029886Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

c ≤ 89 c ≥ 109

1101069490 1029886Monday, October 14, 13

Example 2

A ski resort has several types of hotel rooms and cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per

night. Write and graph a compound inequality that describes the amount a guest would pay per night at the resort.

c = cost per nightRoom Cabin

c ≤ 89 c ≥ 109

{c|c ≤ 89 or c ≥ 109}

1101069490 1029886Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

n− 8 ≤ 14

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

n− 8 ≤ 14 n− 8 ≥ 5

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8

n ≤ 22

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8 +8 +8

n ≤ 22

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8 +8 +8

n ≤ 22 n ≥ 13

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

a. Eight less than a number is no more than fourteen and no less than five.

n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8 +8 +8

n ≤ 22 n ≥ 13

{n|13 ≤ n ≤ 22}

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

−5n > 35

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

−5n > 35 −5n < 10

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

−5n > 35 −5n < 10 −5 −5

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

−5n > 35 −5n < 10

n < −7 −5 −5

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

−5n > 35 −5n < 10

n < −7 −5 −5 −5 −5

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

−5n > 35 −5n < 10

n < −7 n > −2 −5 −5 −5 −5

Monday, October 14, 13

Example 3

Write a compound inequality and solve.

b. The product of negative five and a number is greater than thirty five or less than ten.

n = number

−5n > 35 −5n < 10

n < −7 n > −2

{n|n < −7 or n > −2}

−5 −5 −5 −5

Monday, October 14, 13

Summarizer

Write a compound inequality for which the graph is the empty set and one for which the graph is the set of all real numbers.

Monday, October 14, 13

Problem Sets

Monday, October 14, 13

Problem Sets

Problem Set 1: p. 306 #1-5 all, 7-15 odd

Problem Set 2: p. 306 #16, 17-27 odd, 28, 29, 31, 33-36 all

“It is always easier to believe than to deny. Our minds are naturally affirmative."- John Burroughs

Monday, October 14, 13