3-5 Solve Compound Inequalities
Name
Date
Solve: 3g 6 OR 2g 6
2g
3g 6
OR 6
3
2
3
2
g 2 OR g 3
Use the Division Property of Inequality.
The solution set is {g | g 3 OR g 2} or (, 3] (2, )
Check: Try g 3 and 4
?
?
3(3) 6
OR 2(24) 6
9 . 6 True OR
8 6 True
Graph:
4 3 2 1 0
1
2
3
4
The graph identifies the solutions
of the compound inequality.
Graph each compound inequality. Write the solution set in set-builder
notation and interval notation. Check students’ work.
1. 2 d 5
2. 3 a 3
22 , d AND d # 5
3 2 1 0
3 2 1 0
1
2
1
2
3
4
3
4
23 , a AND a # 3
5
⫺3 ⫺2 ⫺1 0 1 2 3 4 5
⫺3 ⫺2 ⫺1 0 1 2 3 4 5
5
{f | f , 1 or f . 3};
(2`, 1) (3, `)
{a | 23 , a # 3}; (23, 3]
{d | 22 , d # 5}, (22, 5]
4. d 2 OR d > 4
5. 5 x 2
6. 0 x 6
0 # x AND x # 6
25 # x AND x # 2
⫺3 ⫺2 ⫺1 0 1 2 3 4 5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0 1 2 3
{d | d , 22 or d . 4}
(2`, 22) (4, `)
Copyright © by William H. Sadlier, Inc. All rights reserved.
3. f 1 OR f 3
⫺2 ⫺1 0 1 2 3 4 5 6
{x | 25 # x # 2}; [25, 2]
{x | 0 # x # 6}; [0, 6]
Write the inequality for each graph. Write the solution set in set-builder
and interval notation.
7.
2
8.
1
0
1
2
3
1
x . 2 2 AND x , 2
1
So 2 2 , x , 2
1
1
{x | 2 2 , x , 2}; (2 2 , 2)
9.
1
x # 21 OR x $
1
5
2
0
1
1
x . 2 AND x , 1
3
1
So 2 , x , 1
3
1
1
{x | 2 , x , 1}; 2 , 1
3
3
(
10.
0
1
2
3
{x | x # 21 OR x $ 52}; (2`, 21] [52, `)
3
2
1
0
2
)
1
2
3
x , 1.5 AND x $ 22.5
{x | 22.5 # x , 1.5}; [22.5, 1.5)
Lesson 3-5, pages 80–83.
Chapter 3
73
Solve and check the compound inequality. Graph the solution set. Answers may vary. Check students’ answers.
11. 2y 8 6 AND 2y 5 3
12. 3z 7 22 AND 3z 9 3
3z 7 , 22 AND 3z 9 , 3
7 7
9 9
3z , 15 AND 3z , 6
6
3z 15
3z
3 , 3
3 . 3
z , 5 AND
z . 2
2 , z , 5
2y 8 , 6 AND 2y 5 , 3
8 8
5 5
2y , 2 AND 2y , 8
2y 2
2y
8
2 , 2
2 . 2
y , 1 AND
y . 4
4 , y , 1
0
22
1
8
13. 7h 1 20 AND 5h 4 29
25 24 23 22 21 0 1
4
3
9
15. 5 n 15 OR 5 n 20
(
1
4
)
()
( )
17. Juanita is shopping online for a used MP3
Player. She can spend at least $50, but no
more than $210. Shipping and handling will
cost $10.20. If sales tax is 7%, what is
Juanita’s price range for MP3 Players?
Let j price range for MP3 Players
50 # 10.2 1.07j AND 10.2 1.07j # 210
39.8 # 1.07j
AND
1.07j # 199.8
37.20 # j
AND
j # 186.73
So Juanita can spend between $37.20 and
$186.73, inclusive.
7
6 5
6 8
m#
OR 2
8 3
8 6
5
m$
4
3
m $ 1
OR
12
( )
()
( 12 )m # 2( 76 )
0.11 1.1j
.
1.1
1.1
0.1 . j
0.6
1.2j
#
1.2
1.2
OR
0.5 # j
OR
18. Dylan’s mother tells Dylan he must spend
less time playing electronic games. On
1
the weekends he spends 9 2 hours playing
electronic games. If he plays between 13 and
19 hours each week, how many hours does
he play games on weekdays?
Let h hours of play
1
1
13 , 9 5x AND 9 5x , 19
2
2
3.5 , 5x
AND
5x , 9.5
0.7 , x
AND
x , 1.9
Dylan plays between 0.7 and 1.9 hours
on weekdays.
74
The graphs do not overlap. So there is no solution.
0
1
Chapter 3
2
3
4
5
7
3
4
m # 2
12
m#
4.89 . 1.1j 1 5 OR
3.4 $ 4 1.2j
5
5
4 4
0.11 . 1.1j
OR 0.6 $ 1.2j
19. Describe the graph of the compound inequality x 1 AND x 2
and the solution.
1
6
16. 4.89 1.1j 5 OR 3.4 4 1.2j
5
2
5
4
5 3
5 9
n$ n$
2
5
2 15
3 5
3 20
2
3
n#
OR
n$
3
4
( )
5
2
14. 6 m 3 OR 2 m 6
7h 1 $ 20 AND 5h 4 , 29
1 1
4 4
7h $ 21 AND 5h , 25
25
21
5h
7h
5 . 5
7 # 7
h # 3 AND
h . 5
5 , h # 3
2
0
6
Copyright © by William H. Sadlier, Inc. All rights reserved.
5 4 3 2 1
Answers for Algebra I, Practice Book Lesson 3-5, page 74.
14.
2
1
0
15.
0
1
16.
0.5
74A Chapter 3
0
0.5