 Prealgebra 2e

# Chapter 3

Prealgebra 2eChapter 3

### Be Prepared

3.1 3.2

$< <$

3.3

$14 14$

3.3

$20 20$

3.3

$3 + ( − 7 ) 3 + ( − 7 )$

3.4

$5 5$

3.5

$20 − ( − 15 ) 20 − ( − 15 )$

3.6

$11 11$

3.7

$20 ÷ 13 20 ÷ 13$

3.8

$− 15 − 15$

3.9

$− 3 − 3$

3.10

$0 0$

3.11

$16 16$

3.12

$x − 5 x − 5$

### Try It

3.1 3.2 3.3
1. >
2. <
3. >
4. >
3.4
1. <
2. >
3. <
4. >
3.5
1. −4
2. 3
3.6
1. −8
2. 5
3.7

1

3.8

5

3.9
1. −4
2. 4
3.10
1. −11
2. 11
3.11
1. 12
2. −28
3.12
1. 9
2. −37
3.13
1. 17
2. 39
3. −22
4. −11
3.14
1. 23
2. 21
3. −37
4. −49
3.15
1. >
2. >
3. <
4. =
3.16
1. >
2. =
3. >
4. <
3.17
1. 3
2. 18
3.18
1. 11
2. 63
3.19

2

3.20

3

3.21

16

3.22

9

3.23
1. ⓐ −9
2. ⓑ 15
3. ⓒ −20
4. ⓓ 11−(−4)
3.24
1. 19
2. −22
3. −9
4. −8−(−5)
3.25

5 yards

3.26

−30 feet

3.27 6

3.28 7

3.29 −6

3.30 −7

3.31 −2

3.32 −3

3.33 2

3.34 3

3.35

1. 2. 3. 4. 3.36

1. 2. 3. 4. 3.37
1. ⓐ −17
2. ⓑ 57
3.38
1. ⓐ −46
2. ⓑ 26
3.39

−50

3.40

−70

3.41

13

3.42

0

3.43
1. ⓐ 2
2. ⓑ −12
3.44
1. ⓐ 2
2. ⓑ −1
3.45
1. ⓐ −6
2. ⓑ 10
3.46
1. ⓐ −1
2. ⓑ 17
3.47

9

3.48

13

3.49

196

3.50

8

3.51

−7 + 4 = −3

3.52

−8 + (−6) = −14

3.53

[9 + (−16)] + 4 = −3

3.54

[−8 + (−12)] + 7 = −13

3.55

4 degrees Celsius

3.56

−33 feet

3.57

14-yard line

3.58

37-yard line

3.59 2

3.60 3

3.61 −2

3.62 −3

3.63 −10

3.64 −11

3.65 10

3.66 11

3.67    3.68    3.69 −2 4

3.70 −3 3

3.71
1. 8, 8
2. −18, −18
3.72
1. 8, 8
2. −22, −22
3.73
1. 19, 19
2. −4, −4
3.74
1. 23, 23
2. 3, 3
3.75

−29

3.76

−26

3.77

3

3.78

13

3.79

−69

3.80

−47

3.81
1. −2
2. −15
3.82
1. −2
2. −7
3.83
1. −2
2. 36
3.84
1. −19
2. 9
3.85
1. 14 − (−23) = 37
2. −17 − 21 = −38
3.86
1. 11 − (−19) = 30
2. −11 − 18 = −29
3.87

45 degrees Fahrenheit

3.88

9 degrees Fahrenheit

3.89

10,103 feet

3.90

233 feet

3.91
1. $48 2. −$2
3. $18 3.92 1. −$54
2. No, −$5 3.93 1. −48 2. 28 3. −63 4. 60 3.94 1. −56 2. 54 3. −28 4. 39 3.95 1. −9 2. 17 3.96 1. −8 2. 16 3.97 1. −7 2. 39 3.98 1. −9 2. 23 3.99 1. −6 2. 36 3.100 1. −28 2. 52 3.101 −63 3.102 −84 3.103 1. 81 2. −81 3.104 1. 49 2. −49 3.105 29 3.106 52 3.109 21 3.111 39 3.112 13 3.113 −8 3.114 19 3.115 −5 (12) = −60 3.116 8 (−13) = −104 3.117 −63 ÷ −9 = 7 3.118 −72 ÷ −9 = 8 3.119 1. no 2. no 3. yes 3.120 1. no 2. no 3. yes 3.121 −4 3.122 −19 3.123 −6 3.124 −4 3.125 4x = 12; x = 3 3.126 3x = 6; x = 2 3.128 11 3.129 −12 3.130 −9 3.131 x + 7 = −2; x = −9 3.132 y + 11 = 2; y = −9 3.133 p − 2 = −4; p = −2 3.134 q − 7 = −3; q = 4 3.135 132 = −12y; y = −11 3.136 117 = −13z; z = −9 ### Section 3.1 Exercises 1. 3. 5. 1. > 2. < 3. < 4. > 7. 1. < 2. > 3. < 4. > 9. 1. −2 2. 6 11. 1. 8 2. −1 13. 4 15. 15 17. 1. −3 2. 3 19. 1. −12; 2. 12 21. 1. 7 2. 25 3. 0 23. 1. 32 2. 18 3. 16 25. 1. 28 2. 15 27. 1. −19 2. −33 29. 1. < 2. = 31. 1. > 2. > 33. 4 35. 56 37. 0 39. 8 41. 80 43. 1. −8 2. −(−6), or 6 3. −3 4. 4−(−3) 45. 1. −20 2. −(−5), or 5 3. −12 4. 18−(−7) 47. −6 degrees 49. −40 feet 51. −12 yards 53.$3

55.

+1

57.
1. 20,320 feet
2. −282 feet
59.
1. $540 million 2. −$27 billion
61.

Sample answer: I have experienced negative temperatures.

### Section 3.2 Exercises

63. 11

65. −9

67. −2

69. 1

71.

−80

73.

32

75.

−135

77.

0

79.

−22

81.

108

83.

−4

85.

29

87.
1. ⓐ −18
2. ⓑ −87
89.
1. ⓐ −47
2. ⓑ 16
91.
1. ⓐ −4
2. ⓑ 10
93.
1. ⓐ −13
2. ⓑ 5
95.

−8

97.

10

99.

64

101.

121

103.

−14 + 5 = −9

105.

−2 + 8 = 6

107.

−15 + (−10) = −25

109.

[−1 + (−12)] + 6 = −7

111.

[10 + (−19)] + 4 = −5

113.

7°F

115.

−$118 117. −8 yards 119. 25-yard line 121. 20 feet 123. −32 125. Sample answer: In the first case, there are more negatives so the sum is negative. In the second case, there are more positives so the sum is positive. ### Section 3.3 Exercises 127. 6 129. −4 131. −9 133. 12 135. 1. 9 2. 9 137. 1. 16 2. 16 139. 1. 17 2. 17 141. 1. 45 2. 45 143. 27 145. 29 147. −39 149. −48 151. −42 153. −59 155. −51 157. 9 159. −2 161. −2 163. 22 165. 53 167. −20 169. 0 171. 4 173. 6 175. –8 177. −11 179. 1. −3 2. −9 181. 1. 3 2. 7 183. −8 185. −192 187. 1. 3 − (−10) = 13 2. 45 − (−20) = 65 189. 1. −6 − 9 = −15 2. −16 − (−12) = −4 191. 1. −17 − 8 = −25 2. −24 − 37 = −61 193. 1. 6 − 21 = −15 2. −19 − 31 = −50 195. −10° 197. 96° 199. 21-yard line 201.$65

203.

−$40 205.$26

207.

13°

209.

Sample answer: On a number line, 9 is 15 units away from −6.

### Section 3.4 Exercises

211.

−32

213.

−35

215.

36

217.

−63

219.

−6

221.

14

223.

−4

225.

−8

227.

13

229.

−12

231.

−49

233.

−47

235.

43

237.

−125

239.

64

241.

−16

243.

90

245.

−88

247.

9

249.

41

251.

−5

253.

−9

255.

−29

257.

5

259.
1. 1
2. 33
261.
1. −5
2. 25
263.

11

265.

21

267.

38

269.

−56

271.

−3·15 = −45

273.

−60 ÷ (−20) = 3

275.

$−6 a + b −6 a + b$

277.

−10 (pq)

279.

−\$3,600

281.

Sample answer: Multiplying two integers with the same sign results in a positive product. Multiplying two integers with different signs results in a negative product.

283.

Sample answer: In the first expression the base is positive and after you raise it to the power you should take the opposite. Then in the second expression the base is negative so you simply raise it to the power.

### Section 3.5 Exercises

285.
1. no
2. no
3. yes
287.
1. no
2. no
3. yes
289.

n = −7

291.

p = −17

293.

u = −4

295.

h = 6

297.

x = −16

299.

r = −14

301.

3x = 6; x = 2

303.

2x = 8; x = 4

305.

x = 9

307.

c = −8

309.

p = 3

311.

q = −12

313.

x = 20

315.

z = 0

317.

n + 4 = 1; n = −3

319.

8 + p = −3; p = −11

321.

a − 3 = −14; a = −11

323.

−42 = −7x; x = 6

325.

−15f = 75; f = −5

327.

−6 + c = 4; c = 10

329.

m − 9 = −4; m = 5

331.
1. x = 8
2. x = 5
333.
1. p = −9
2. p = 30
335.

a = 20

337.

m = 7

339.

u = −52

341.

r = −9

343.

d = 5

345.

x = −42

347.

349.

Sample answer: It is helpful because it shows how the counters can be divided among the envelopes.

351.

Sample answer: The operation used in the equation is multiplication. The inverse of multiplication is division, not addition.

### Review Exercises

353. 355. 357. 359.

<

361.

>

363.

>

365.

−6

367.

4

369.
1. −8
2. 8
371.
1. −32
2. 32
373.

21

375.

36

377.

0

379.

14

381.

−33

383.

<

385.

=

387.

55; −55

389.

7

391.

54

393.

−1

395.

−16

397.

−3

399.

−10°

401.

10

403.

1

405.

96

407.

−50

409.

−1

411.

21

413.
1. 3
2. −16
415.

−27

417.

−8 + 2 = −6

419.

10 + [−5 + (−6)] = −1

421.

16 degrees

423. 5

425. 7

427.

8

429.

−38

431.

−58

433.

−1

435.
1. −2
2. −11
437.

41

439.

−12 − 5 = −17

441.

−2 degrees

443.

−36

445.

121

447.

−7

449.

−8

451.

−45

453.

−9

455.

−81

457.

54

459.

4

461.

−66

463.

−58

465.

−12(6) = −72

467.
1. no
2. yes
3. no
469.

−12

471.

−7

473.

3x = 9; x = 3

475.

9

477.

4

479.

−6y = −42; y = 7

481.

m + 4 = −48; m = −52

483.

### Practice Test

485.
1. <
2. >
487.
1. 7
2. −8
489.

5

491.

−27

493.

11

495.

54

497.

−8

499.

22

501.

39

503.

34

505.

−7 − (−4) = −3

507.

4°F

509.

n = −1

511.

r = 6

513.

y − 8 = −32; y = −24 Do you know how you learn best?
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