Prealgebra

# Chapter 3

PrealgebraChapter 3

## Try It

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

3.36

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 pounds 119. 25-yard line 121. 20 calories 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. 5.2 177. −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.

8

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 one expression the base is positive and then we take the opposite, but in the other the base is negative.

## Section 3.5 Exercises

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

−7

291.

−17

293.

−4

295.

6

297.

−16

299.

−14

301.

3x = 6; x = 2

303.

2x = 8; x = 4

305.

9

307.

−8

309.

3

311.

−12

313.

20

315.

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.

f(−15) = 75; f = 5

327.

−6 + c = 4; c = 10

329.

m − 9 = −4; m = 5

331.
1. 8
2. 5
333.
1. −9
2. 30
335.

20

337.

7

339.

−52

341.

−9

343.

5

345.

−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

470.

−6

471.

−7

472.

−32

473.

3x = 9; x = 3>

475.

9

477.

4

479.

−6y = −42; y = 7

481.

m + 4 = −48; m = −52

## 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

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