Answers for Lesson 4-1, pp. 171–172 Exercises
1. An algebraic expression differs from a numerical expression
because it contains at least one variable, and the value
changes.
2. subtraction
3. addition
Exercises 4–7. Answers may vary. Samples are given:
4. three less than w
5. the product of five and w
6. twelve more than w
7. the quotient of w and four
8. 10
9. 6
11. 6
12. s 4
14. t 11
15. 5q
10. 14
p
13. 5
16. 7h
Exercises 17–24. Answers may vary. Samples are given:
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17. two more than a number
18. four divided by a number
19. nine and one tenth less than a number
20. a number subtracted from six and five tenths
21. one and three tenths times a number
22. ten more than a number
23. a number divided by ten
24. three and five tenths times a number
25. 42
26. 24.4
27. 3
28. 3
29. 10
30. 15
31. $110.25w
32. n 5
33. 10n
34. 60n; 1,200
Course 2
Chapter 4
37
Answers for Lesson 4-1, pp. 171–172 Exercises (cont.)
35. Answers may vary. Sample: Multiply 24(60) to find the number
of minutes in 24 h. Then multiply the answer by 1,260, the
number of beats per minute. The heart beats 1,814,400 times
in 24 h.
36. Answers may vary. Sample: Candles cost $10 each. How
much do you pay for n candles?
37. Subtraction is not commutative.
38. 440p
39. Answers may vary. Sample: The second student charges $15
to start and $3/h.
40. D
41. F
42. 11.9
43. 45
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44. 50
Course 2
Chapter 4
38
Answers for Lesson 4-2, pp. 176–177 Exercises
1. solution
2. B
3. yes
4. yes
5. no
6. 9
7. 3
8. 5
9. 4
10. 39
11. 288
12. 6.1
13. 65
14. 3.9
15. 8
16. 15.5
17. 4
18. 24
19. 8.4
20. about 7
21. about 19
22. about 30
23. about 3 bowling pins
24. 85 n 103; about 18 lb
25. 55b 2,000; 36 boxes
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26. Check students’ work.
27. 54
28. 37
29. 20
30. 44
31. 563
32. 20
33. 4d 360
34. No; an expression has no equal sign in order to compare
values.
35. 31.89 in.
36. 10.01 in.
37. 4c 67.80; about $17; no; the total should be about 4($12.95),
or $51.80.
38. C
39. H
40. 4
41. 1
42. 10
Course 2
Chapter 4
39
Answers for Lesson 4-3, pp. 183–184 Exercises
1. Inverse
2. Jean. Dylan’s error was adding 4 to both sides instead of
subtracting.
3. 12
4. 8
5. 49
6. 200
7. 205.4
8. 5.8
9. 5
10. 56
11. 12
12. 309.9
13. 178
14. 472
15. 11
16. 139.5
17. $5,300
Exercises 18–21. Check students’ work.
18. 11.5
19. 9
20. 88
21. 80.8
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22. 133 r 62; 71 beats/min
23. 15 p 33; 18 points
24. 12 b 9; 21 ladybugs
25. B
27. A
26. D
28. C
29. 343 a 1,166; 1,509 m/s
30. Subtract 2 from each side; Subtraction Property of Equality.
31. 119
11
32. 18
33. 0.9
1
34. 117
35. 116
21
37. p 8.45 21.50; $29.95
11
36. 12
38. She has saved $135. The camp costs $250. She needs d
dollars.
39. Let r the number of runs needed;
3 4 2 6 8 r 30; 7 runs.
40. D
41. H
42. C
43. 33
44. 23
Course 2
Chapter 4
40
Answers for Lesson 4-4, pp. 188–190 Exercises
1. Multiplication Property of Equality
2. 10 3x; 10
3
3. Division Property of Equality
4. Multiplication Property of Equality
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5. Division Property of Equality
6. B
7. C
8. A
9. 12
10. 4
11. 5
12. 42
13. 20
14. 16
15. 3
16. 6
17. 14
18. 100
19. 87
20. 96
21. 4 h
22. 5 days
23. 24
24. 27
25. 100.8
26. 2.8
27. 30
28. 5.5
29. 6
30. 144
31. 5.5
32. 39.5
33. 25.5
34. 20.5
35. 12 gal
36. about 1,979 lb of apples
37. m represents the money the quintet needs to earn, 5
represents each member, and 50 represents the money each
member receives.
38. 12 x 36; 36 is the multiple of 12 that is closest to
38; x N 3.
39. 50
40. 43.26
41. 85
42. 128.7
1
43. 213
44. 16.2342
45. 15 yr
46. about 198 plays
Course 2
Chapter 4
41
Answers for Lesson 4-4, pp. 188–190 Exercises (cont.)
47. b is the reciprocal of a, and b u 0.
48. Answers may vary. Sample: The student may have divided 12
by 6. The student should have multiplied both sides by 6 to
get n 72.
49–51. Check students’ work.
52. 100 20w 1,000; 45 weeks
53. 72
54. 1.1
55. 23
28
56. 141
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1
57. 12
Course 2
Chapter 4
42
Answers for Lesson 4-5, pp. 196–198 Exercises
1. A one-step expression uses only one operation, while a twostep expression uses two.
2. 16 4x 12; 7
3. B
4. A
5. C
6. 12
7. 70
8. Let p number of points scored before; 3p 2.
9. Let h your height; 6h 1.
p
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10. Let p number of pages; 2 7.
11. Let w weight; 5w 8.
12. Let d distance; 2d 100.
13. 1.5
14. 17.2
15. 0.9
16. 20
17. 20
18. 63
19. 14.7
20. 3.2
21. 15.2
22. 10
23. 7
24. 3
25. 9
26. 1
27. Let m number of months; 19m 75; $227.
28. 4 wk
29. $40 is the hourly rate, h is the number of hours the electrician
works, $35 is the fee for a house call, and $115 is the total bill.
The electrician works 2 h.
30. $12
31. Check students’ work.
32. 3.1
33. 11.5
34. 6
35. 45
36. 10
37. 20
38. Let m number of months; 40m 35; $435.
Course 2
Chapter 4
43
Answers for Lesson 4-5, pp. 196–198 Exercises (cont.)
39. 9 min
40. 130 mi
41. Answers may vary. Sample: You need to keep the equation
“balanced.”
42. 11 min/mi
43. C
44. J
45. D
46. R
47. © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
48. S
Course 2
Chapter 4
44
Answers for Lesson 4-6, pp. 202–204 Exercises
1. Let m number of miles; 2.00 0.50m 5.00; 6 mi.
2. 4
3. 12
4. 136
5. 3
6. 1.5
7. 8
8. 14
9. 1
10. 1
11. 12
12. 1.1
14. 29
80
15. 119
36
13. 2 34
16. 6
17. 15
18. 8
19. 72
20. 49
21. 121
22. 18
23. 37.8
24. 2 58
27. 550
25. 4
7
26. 44
28. 39
29. Let r number of roses; 5.99 1.25r 20.99; 12 roses.
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30. Let h number of hours; 10 22h 98; 4 h.
31. Let h number of additional hours; 3.95 1.25h 7.70; 3 h.
32. Let h number of hours; 20h 3 117; 6 h.
33. Let x measure of each angle; 45 2 x 180; 67.5 .
34. Let n number of countries; 14n 6 202; 14 countries.
37. 8 23
38. 30 the DJ’s hourly wage; x hours the DJ works; 65 cost
of decorations; 170 amount of money budgeted
35. 11
36. 15
39. 15 credits
40. 45 cents
41. Check students’ work.
42. $.90/lb
43. B
44. J
45. C
46–48. Check students’ work.
Course 2
Chapter 4
45
Answers for Lesson 4-7, pp. 207–208 Exercises
1. inequality
2. no; 4 R 4
3. C
4. 1, 0
5. 1
6. 1
7. 2
8. 1
9. 12
10. 10
11.
12.
2 3 4 5 6 7
13.
14.
5 4 3 2 1 0
2 1 0 1 2 3
15.
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17.
6 5 4 3 21
16.
2 1 0 1 2 3
7 6 5 4 32
18.
7 6 5 4 32
9 8 7 6 54
19. x K 6
20. x R 2
21. x L 1
22. x K 1
23. c K 1.00
24. x L 30
25. a L 17;
15 16 17 18 19 20
26. n S 100;
98 99 100 101 102 103
27. p K 0;
28. s K 65;
3 2 1 0 1 2
50
60
70
29. Use an open circle for R or S and use a closed circle for K
or L.
30. Answers may vary. Sample: 17 is to the right of 22 on a
number line.
31. w K 3
32. p K 2
33. 3, 2, or 1
34. 1, 0, or 1
Course 2
Chapter 4
46
Answers for Lesson 4-7, pp. 207–208 Exercises (cont.)
35. 6, 5, or 4
36. L
37. B
38. H
39. 4, 2, 1, 2, 4, 7
40. 9, 8, 6, 3, 12
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41. 5, 2, 0, 7, 10
Course 2
Chapter 4
47
Answers for Lesson 4-8, pp. 212–214 Exercises
1. Addition Property of Inequality
2. 5
3. C
4. D
5. B
6. A
7. g K 6;
9 8 7 6 54
8. m S 21;
9. y L 16;
23
14
10. x S 4;
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16
19
18
6 5 4 3 21
11. n K 27;
12. p R 0;
21
25
27
29
3 2 1 0 1 2
13. y L 17;
15 16 17 18 19
14. q R 6;
4
15. b S 2;
4
16. h R 21;
17. n L 1;
18. r S 5;
19. p K 4;
Course 2
5
6
7
8
2
23
0
21
19
1 0 1 2 3 4
7 6 5 4 32
7 6 5 4 32
Chapter 4
48
Answers for Lesson 4-8, pp. 212–214 Exercises (cont.)
20. b S 23;
21. f L 5;
22. m S 1;
23. x R 1;
25
23
21
7 6 5 4 32
1
0
1
2
3
1
0
1
2
3
24. k K 11;
–13
–11
–9
25. Let s amount of money to save; s 35 L 100; s L 65; you
need to save at least $65.
26. 32,000 R 75,000; R 43,000
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27. 109 x L 212; x L 103
28. h R 10.3
29. w S 21
30. x L 93
31. j L 5
32. k L 6
33. a R 5 21
34. 15 n S 10; n S 5
35. No; the solution of x 5 K 2 is x K 7, and the solution of
2 K x 5 is x L 7.
36. d 2.1 S 2.25; d S 0.15
37. p L 338; they must score at least 420 82, or 338, points.
38. 7 K x R 5
39. no more than 1,220 Cal
40. 15.6
41. 1.48
42. 2.06
43. 16
5
44. 27
4
45. 33
4
46. 61
8
Course 2
Chapter 4
49
Answers for Lesson 4-9, pp. 216–218 Exercises
1. The inequality symbol is reversed.
3. S
2. D
4. L
5. S
6. h R 4;
1 2 3 4 5 6
7. p S 12;
10 11 12 13 14 15
8. n K 3;
9. x R 8;
6 5 4 3 2 1
1110 9 8 7 6
10. b K 3;
0 1 2 3 4 5
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11. w L 6;
8 7 6 5 4 3
12. d K 7;
13. t R 5;
4 5 6 7 8 9
8 7 6 5 4 3
14. g R 7;
15. p L 5;
16. y R 6.1;
9
7
5
7
5
3
6.4
6.2
6
6
6.5
7
17. w L 6.5;
18. at least 50 pages
19. p R 15;
Course 2
17
15
13
Chapter 4
50
Answers for Lesson 4-9, pp. 216–218 Exercises (cont.)
20. k L 24;
22 23 24 25 26 27
21. w K 21;
22. y S 56;
23
58
21
56
19
54
23. n R 10;
7 8 9 10 11 12
24. m L 30;
25. x R 40;
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26. c K 10;
27. x S 80;
28. g L 8.4
29. p S 16.8
30. f K 27.5
32
42
30
28
40
38
7 8 9 10 11 12
85
80
75
8.6
8.4
8.2
17 16.8 16.6
28 27.5
27
31. c 70 K 6,000; at most 85 cases
32. at least 278 times
33. at most 4 pies
34. 3x S 12; x R 4
35. 4x K 44; x K 11
36. x9 R 10; x S 90
37. 5x L 8; x L 40
38. 2n R 10; n R 5
Course 2
Chapter 4
51
Answers for Lesson 4-9, pp. 216–218 Exercises (cont.)
39. To solve 5x R 25, divide each side by 5 and reverse the
inequality symbol. To solve 5x R 25, divide each side by 5 but
do not reverse the symbol.
40. 1.1 S x
41. 50.2 R t
42. 0.7 L p
43. at most 3 hot dogs
44. at most 12 bags of peanuts
45. 4 bags of peanuts; $.50
46. at most 6 refrigerators
47. The student should not have reversed the inequality symbol.
48. 18 L 2y, y L 9; 2y R 18, y S 9; no; y 9 is not a
solution to the second inequality.
7 8 9 10 11 12
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49. 3x 10 S 19; x R 3;
7 8 9 10 11 12
6 5 4 3 2 1
50. A
51. G
52. 4.875; 4; 4
53. 3.83; 3.6; 2.2
Course 2
Chapter 4
52