Name ———————————————————————
Practice A
LESSON
5.4
LESSON 5.4
Date ————————————
For use with the lesson “Solve Compound Inequalities”
Write an inequality that is represented by the graph.
1.
2.
0
1
2
3
4
5
6
7
8
9
24
23
22
21
0
1
2
3
4
26
25
24
23
22
21
0
1
2
3.
24
23
22
21
0
1
2
3
4
24
23
22
21
0
1
2
3
4
28
27
26
25
24
23
22
21
0
4.
5.
6.
Sketch a graph of the inequality.
9. x < 26 or x r 2
8. 1 b x b 5
10. x < 8 or x > 11
11. 14 > x > 9
12. x r 4 or x b 0
13. x < 22 or x > 4
14. 23 < x < 4
15. x > 23 or x < 28
16. x b 26 or x r 21
Translate the verbal phrase into an inequality. Then graph the inequality.
17. All real numbers that are less than 3 and greater than 0
5-46
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
7. 23 < x < 7
Algebra 1
Chapter Resource Book
CS10_CC_A1_MECR710723_C5L04PA.indd 46
5/13/11 10:45:40 PM
Name ———————————————————————
LESSON
5.4
Date ————————————
Practice A
continued
For use with the lesson “Solve Compound Inequalities”
LESSON 5.4
18. All real numbers that are greater than 7 or less than 1
19. All real numbers that are greater than or equal to 22 and less than 4
Solve the inequality. Graph your solution.
20. 0 < x 1 6 b 15
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
21. 2x 2 1 < 3 or 2x 1 1 r 11
22. Turnpike The Pennsylvania Turnpike Commission requires that all over-sized
vehicles get a permit to travel on the roadway. A vehicle is considered over-sized
if it is over 10 feet in width. However, the maximum width of a vehicle that the
commission will allow on the roadway is 11.5 feet.
a. Write a compound inequality that
represents the widths w of over-sized
vehicles that can travel on the
Pennsylvania Turnpike.
b. Graph the inequality.
23. Elevations The highest point in the United States is Mount McKinley in Alaska at
an elevation of 6198 meters. The lowest point in the United States is Death Valley,
California at an elevation of 286 meters.
a. Write a compound inequality that
represents the possible elevations e
of land in the United States.
b. Graph the inequality.
24. Radar A ship uses radar to detect approaching planes.
A plane is shown as a blip on the radar. Use the diagram
to write an inequality that describes the distance d of the
plane from the ship.
25 km
20 km
15 km
10 km
5 km
Plane
Algebra 1
Chapter Resource Book
CS10_CC_A1_MECR710723_C5L04PA.indd 47
5-47
5/13/11 10:45:41 PM
Lesson 5.3 Solve Multi-Step
Inequalities, continued
1. x r 1;
24
23
2. p > 26;
3. n r 24;
4. d < 4;
5. y < 24;
22
0
21
2
3
4
22
0
2
4
6
8
28
26
24
22
0
2
4
6
8
24
26
0
22
24
2
0
22
1
6. a b 2};
4
2
8. d > 212;
4
2
6
4
0
1
6
1
0
2
4
6
8
216 212 28
24
0
4
8
12
24
16
18. z r 23 19. no solution 20. all real numbers
1
21. c > 2} 22. no solution 23. no solution
3
24. all real numbers 25. all real numbers
26. no solution
27. 4x 1 2x < 5x 2 13; x < 213;
213
26
24
22
9
28. 3(2x 1 1) r 22(3 1 x); x r 2};
8
9
8
0
1
2
29. 2(5 2 x) b 5x 1 3x; x r 1;
23
22
21
0
1
2
3
4
30. 32 2 4x b 24(28 2 x); x r 0;
28
26
24
22
0
2
4
6
8
1
31. 3(2 2 4x) b 5x 1 7x; x r } ;
4
1
4
23
22
21
0
22
0
2
4
6
8
10 12 14
6.1
0
2
4
6
8
10
1
1. sometimes true; true if a 5 5, b 5 1, c 5 2},
2
and d 5 21; false if a 5 2, b 5 1, c 5 21, and
d 5 22 2. always true 3. always true 4. never
true 5. sometimes true; true if a 5 2, b 5 1,
1
c 5 21, and d 5 22; false if a 5 1, b 5 }2,
432
c 5 21, and d 5 22 6. xy b 432; x b }
y
7. 54 in. and 108 in. 8. yes; 36 in.
864
9. 2x 1 } b 100 10. yes; 4 in.
x
Lesson 5.4 Solve Compound
Inequalities
Teaching Guide
; The graphs intersect
for all numbers less than 4 and greater than 21.
2.
; If 3 is a solution of
22 21 0 1 2 3 4 5
x > 21, it must also be a solution of x < 4 because
3 lies between 21 and 4.
3.
; The graphs do not
22 21 0 1 2 3 4 5
intersect.
4. If 4 is a solution of x r 3, it is not also a
solution of x < 0 because 4 lies only to the right
of 3.
1.
22 21
0
1
2
3
4
5
Practice Level A
1
2
3
32. a. 5d 2 250 > 0 b. more than 50 daffodils
c. Yes, because they need at least 50 daffodils
to sell. 33. a. 0.06( p 2 50)
b. ( p 2 50) 1 0.06( p 2 50) b 1000; p b 993.40
A58
7
Challenge Practice
16. all real numbers 17. no solution
28
6
3. 16.9x 1 40 r 0
2
13. no solution 14. no solution 15. no solution
24
5
1. 3.5x 1 40 r 0 2. 29.6x 1 108 r 0
11. all real numbers 12. no solution
1
4
Interdisciplinary Application
8
9. all real numbers 10. no solution
2
3
9. 6 r 24, all real numbers
8
22
218 216 214 212 210
2
4. x > 6 5. 3 b x 6. x < 28 7. 24 > 1, no
solutions 8. 213 < 26, all real numbers
1
26
1
22
4
28
0
3. x < 6.1;
24
28
7. m r 4;
1
26
26
21
2. 8 b x;
28
28
1. x > 2;
Algebra 1
Chapter Resource Book
1. 4 b x b 8 2. x < 23 or x > 0 3. 21 b x < 3
4. x < 0 or x r 3 5. 24 < x b 0
6. x b 26 or x > 23
7.
23
24
7
22
0
2
4
6
8
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
ANSWERS
Practice Level C
Study Guide
Lesson 5.4 Solve Compound
Inequalities, continued
8.
0
21
28
26
1
2
24
3
4
5
0
22
0
22
2
4
6
8
10
26
7. 3 b x < 7;
4
9
24
15.
16.
22
0
21
23
22
0
21
1
1
2
2
0
3
3
1
4
2
3
5
210 29 28 27 26 25 24 23 22 21
0
0
28 27 26 25 24 23 22 21
24
23
22
0
22 21
1
2
3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
20. 26 < x b 9;
1
0
1
0
21
1
2
3
6
7
8
24
23
22
21
0
1
2
3
4
212 29
26
23
0
3
6
9
12
5
6
3
4
9
10
2000
11
3
4
5
6
29 28 27 26 25 24 23 22 21
0
1
5
6
13
14
15
16
17
3000
4000
5000
6000
7000
9
4
0
1
2
0
1
2
3
4
2
3
26
1
26
24
0
22
2
4
0
1
2
3
4
5
6
0
1
2
7
3
6
8
9
4
5
6
95
0
10 20 30 40 50 60 70 80 90 100
26
0
2. 21 < x < 7;
4
5
4. 21 < x < 3;
24
3
22
4
0
22
0
1
2
3
2
4
5
4
6
7
24
24
23
6
8
9
22
26
2
24
22 21
9
19
3. 2} < x b };
2
2
6
3.5
0
0
Practice Level C
11
11
1. 2} b x < 4; 2 2
2
22.5
4. 24 < x b 4;
8
17. x b 4 or x > 8 18. a. 2 mi b. 8 mi
c. 2 b d b 8
3. 22.5 b x < 3.5;
21
7
16. 25 b T b 95
2. x b 21 or x > 5;
22
3
25
210 29 28 27 26 25 24 23 22 21
23
6
14. 23 < 2x 2 5 b 11; 1 < x b 8;
24 23 22 21
12
1. 28 b x b 23;
1
5
15. 25 < 3x 1 1 b 10; 22 < x b 3;
Practice Level B
0
6
13. x 2 1 < 21 or 3 1 x r 7; x < 0 or x r 4;
24. Sample answer: 15 < d < 20
24
8
210
21
4
7
6198
1000
3
6
22 21
286
0
2
210 29 28 27 26 25 24 23 22 21
23. a. 286 b e b 6198;
22
2
24 23 22 21
4
5
2
8
4
4
11.5
7
1
2
12. 221 < 3x < 26; 27 < x < 22;
b.
6
0
22 21
0
22
23
22. a. 10 < w b 11.5;
5
24
5
2
21. x < 2 or x r 5;
21
12
4
11. x b 2} or x > 3;
3
4
19. 22 b x < 4;
10
10. x < 26 or x > 23;
5
18. x < 1 or x > 7;
b.
1
4
4
25 24 23 22 21
17. 0 < x < 3;
22
0
24 23 22 21
13.
14.
23
8
9. x < 21 or x r 4;
10 11 12 13 14 15 16 17
12.
6
14
22 21
8
4
8. x < 2 or x > 5;
12
11.
7
2
1
6
2
0
22
6. 24 b x < 1;
11
10.
1
ANSWERS
9.
22
5. 1 < x < 10;
9
19
2
0
22
22
2
21
4
0
6
1
8
2
10
3
12
4
5. x < 29 or x > 7;
0
2
4
6
29
210 28 26 24 22
7
0
2
4
6
8
10
Algebra 1
Chapter Resource Book
A59