Alg1bsection5 4podcast-131015074630-phpapp02

Section 5-4
Compound 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
time
2. Intersection: A compound inequality the connects the two
inequalities using and; Only true if BOTH inequalities are true
3. Union:

Vocabulary
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

Example 1
a. 7 < x + 2 ≤ 11
Solve and graph the solution set.

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11and

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11
−2 −2
and

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11
−2 −2
5 < x
and

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11
−2 −2 −2 −2
5 < x
and

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11
−2 −2 −2 −2
5 < x x ≤ 9
and

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11
−2 −2 −2 −2
5 < x x ≤ 9
and
1050

Example 1
a. 7 < x + 2 ≤ 11
7 < x + 2 x + 2 ≤ 11
−2 −2 −2 −2
5 < x x ≤ 9
and
{x|5 < x ≤ 9}
1050

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30or

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30
+7 +7
or

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30
+7 +7
4k ≤ 32
or

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30
+7 +7
4k ≤ 32
or
4 4

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30
+7 +7
4k ≤ 32
or
4 4
k ≤ 8

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30
+7 +7 −12 −12
4k ≤ 32
or
4 4
k ≤ 8

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30
+7 +7 −12 −12
4k ≤ 32 −9k ≥ 18
or
4 4
k ≤ 8

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
4k − 7 ≤ 25 12 − 9k ≥ 30
+7 +7 −12 −12
4k ≤ 32 −9k ≥ 18
or
4 4
k ≤ 8
−9 −9

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
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
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
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 42

Example 1
b. 4k − 7 ≤ 25 or 12 − 9k ≥ 30
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 42

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5or

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5
−5 −5
or

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5
−5 −5
−y ≥ 4
or

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5
−5 −5
−y ≥ 4
or
−1 −1

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5
−5 −5
−y ≥ 4
or
−1 −1
y ≤ −4

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5
−5 −5 −4 −4
−y ≥ 4
or
−1 −1
y ≤ −4

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5
−5 −5 −4 −4
−y ≥ 4 3y < −9
or
−1 −1
y ≤ −4

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−y + 5 ≥ 9 3y + 4 < −5
−5 −5 −4 −4
−y ≥ 4 3y < −9
or
−1 −1
y ≤ −4
3 3

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−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
c. − y + 5 ≥ 9 or 3y + 4 < −5
−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 20

Example 1
c. − y + 5 ≥ 9 or 3y + 4 < −5
−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 20

Example 1
d. d − 3 < 6d +12 < 2d + 32

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12 6d +12 < 2d + 32

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12 6d +12 < 2d + 32and

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12 6d +12 < 2d + 32
−d −d
and

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12 6d +12 < 2d + 32
−d −d
−3 < 5d +12
and

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12 6d +12 < 2d + 32
−d −d
−3 < 5d +12
and
−12 −12

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12 6d +12 < 2d + 32
−d −d
−3 < 5d +12
and
−12 −12
−15 < 5d

Example 1
d. d − 3 < 6d +12 < 2d + 32
d − 3 < 6d +12 6d +12 < 2d + 32
−d −d
−3 < 5d +12
and
5 5
−12 −12
−15 < 5d

Example 1
d. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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. d − 3 < 6d +12 < 2d + 32
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 night
Room

Example 2
c = cost per night
Room Cabin

Example 2
c = cost per night
Room Cabin
c ≤ 89

Example 2
c = cost per night
Room Cabin
c ≤ 89 c ≥ 109

Example 2
c = cost per night
Room Cabin
c ≤ 89 c ≥ 109
1101069490 1029886

Example 2
c = cost per night
Room Cabin
c ≤ 89 c ≥ 109
{c|c ≤ 89 or c ≥ 109}
1101069490 1029886

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
ﬁve.
n = number

Example 3
ﬁve.
n = number
n − 8 ≤ 14

Example 3
ﬁve.
n = number
n − 8 ≤ 14 n − 8 ≥ 5

Example 3
ﬁve.
n = number
n − 8 ≤ 14 n − 8 ≥ 5
+8 +8

Example 3
ﬁve.
n = number
n − 8 ≤ 14 n − 8 ≥ 5
+8 +8
n ≤ 22

Example 3
ﬁve.
n = number
n − 8 ≤ 14 n − 8 ≥ 5
+8 +8 +8 +8
n ≤ 22

Example 3
ﬁve.
n = number
n − 8 ≤ 14 n − 8 ≥ 5
+8 +8 +8 +8
n ≤ 22 n ≥ 13

Example 3
ﬁve.
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
or less than ten.
n = number

Example 3
or less than ten.
n = number
−5n > 35

Example 3
or less than ten.
n = number
−5n > 35 −5n < 10

Example 3
or less than ten.
n = number
−5n > 35 −5n < 10
−5 −5

Example 3
or less than ten.
n = number
−5n > 35 −5n < 10
n < −7
−5 −5

Example 3
or less than ten.
n = number
−5n > 35 −5n < 10
n < −7
−5 −5 −5 −5

Example 3
or less than ten.
n = number
−5n > 35 −5n < 10
n < −7 n > −2
−5 −5 −5 −5

Example 3
or less than ten.
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

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