algebra 1b section 5-4

Section 5-4Compound Inequalities

Monday, October 14, 13

Essential Question

✤ How do you solve compound inequalities?


Vocabulary

1. Compound Inequality:

2. Intersection:

3. Union:


Vocabulary

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

2. Intersection:

3. Union:


Vocabulary


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

3. Union:


Vocabulary


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


Example 1

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


Example 1


7 < x + 2


Example 1


7 < x + 2 x + 2 ≤ 11


Example 1


7 < x + 2 x + 2 ≤ 11and


Example 1


7 < x + 2 x + 2 ≤ 11 −2 −2

and


Example 1


7 < x + 2 x + 2 ≤ 11 −2 −2

5 < x

and


Example 1


7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x

and


Example 1


7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and


Example 1


7 < x + 2 x + 2 ≤ 11 −2 −2 −2 −2

5 < x x ≤ 9

and

1050Monday, October 14, 13

Example 1


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.


Example 1


4k − 7 ≤ 25


Example 1


4k − 7 ≤ 25 12− 9k ≥ 30


Example 1


4k − 7 ≤ 25 12− 9k ≥ 30or


Example 1


4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7

or


Example 1


4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 4k ≤ 32

or


Example 1


4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 4k ≤ 32

or

4 4


Example 1


4k − 7 ≤ 25 12− 9k ≥ 30 +7 +7 4k ≤ 32

or

4 4 k ≤ 8


Example 1


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

or

4 4 k ≤ 8


Example 1


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

or

4 4 k ≤ 8


Example 1


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

or

4 4 k ≤ 8

−9 −9


Example 1


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

or

4 4 k ≤ 8

−9 −9 k ≤ −2


Example 1


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


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.


Example 1


−y + 5 ≥ 9


Example 1


−y + 5 ≥ 9 3y + 4 < −5


Example 1


−y + 5 ≥ 9 3y + 4 < −5or


Example 1


−y + 5 ≥ 9 3y + 4 < −5 −5 −5

or


Example 1


−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −y ≥ 4

or


Example 1


−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −y ≥ 4

or

−1 −1


Example 1


−y + 5 ≥ 9 3y + 4 < −5 −5 −5 −y ≥ 4

or

−1 −1 y ≤ −4


Example 1


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

or

−1 −1 y ≤ −4


Example 1


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

or

−1 −1 y ≤ −4


Example 1


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

or

−1 −1 y ≤ −4

3 3


Example 1


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

or

−1 −1 y ≤ −4

3 3 y < −3


Example 1


−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


−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.


Example 1


d − 3 < 6d +12


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32and


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

and


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

−12 −12


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

−12 −12 −15 < 5d


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

5 5

−12 −12 −15 < 5d


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

5 5 −3 < d

−12 −12 −15 < 5d


Example 1


d − 3 < 6d +12 6d +12 < 2d + 32 −d −d

−3 < 5d +12

and

5 5 −3 < d

−12 −12 −15 < 5d

d > −3


Example 1


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


Example 1


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


Example 1


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


Example 1


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


Example 1


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


Example 1


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


Example 1


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


Example 1


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


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.


Example 2



c = cost per night


Example 2



c = cost per nightRoom


Example 2



c = cost per nightRoom Cabin


Example 2




c ≤ 89


Example 2




c ≤ 89 c ≥ 109


Example 2




c ≤ 89 c ≥ 109

1101069490 1029886Monday, October 14, 13

Example 2




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.


Example 3



n = number


Example 3



n = number

n− 8 ≤ 14


Example 3



n = number

n− 8 ≤ 14 n− 8 ≥ 5


Example 3



n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8


Example 3



n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8

n ≤ 22


Example 3



n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8 +8 +8

n ≤ 22


Example 3



n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8 +8 +8

n ≤ 22 n ≥ 13


Example 3



n = number

n− 8 ≤ 14 n− 8 ≥ 5 +8 +8 +8 +8

n ≤ 22 n ≥ 13

{n|13 ≤ n ≤ 22}


Example 3


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


Example 3



n = number


Example 3



n = number

−5n > 35


Example 3



n = number

−5n > 35 −5n < 10


Example 3



n = number

−5n > 35 −5n < 10 −5 −5


Example 3



n = number

−5n > 35 −5n < 10

n < −7 −5 −5


Example 3



n = number

−5n > 35 −5n < 10

n < −7 −5 −5 −5 −5


Example 3



n = number

−5n > 35 −5n < 10

n < −7 n > −2 −5 −5 −5 −5


Example 3



n = number

−5n > 35 −5n < 10

n < −7 n > −2

{n|n < −7 or n > −2}

−5 −5 −5 −5


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.


Problem Sets


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


algebra 1b section 5-4

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