Lynn Marecek; MaryAnne Anthony-Smith

Chapter 2

Try It

2.1

no

2.2

yes

2.3

$x = −46$

2.4

$x = −50$

2.5

$n = −14$

2.6

$p = −32$

2.7

$p = \frac{9}{6} p = \frac{3}{2}$

2.8

$q = \frac{4}{3}$

2.9

$b = −1.63$

2.10

$c = −3.67$

2.11

$y = 15$

2.12

$z = 2$

2.13

$p = 5$

2.14

$q = −16$

2.15

$h = 6$

2.16

$x = 2$

2.17

$x + 10 = 41; x = 31$

2.18

$y - 12 = 51; y = 63$

2.19

$4 x - 3 x = 14; x = 14$

2.20

$7 a - 6 a = −8; a = −8$

2.21

7 pounds

2.22

42 books

2.23

$20,900

2.24

$11.00

2.25

$y = \frac{−41}{3}$

2.26

$z = \frac{−55}{4}$

2.27

$a = 294$

2.28

$b = 144$

2.29

$k = −8$

2.30

$g = −3$

2.31

$n = 35$

2.32

$y = 18$

2.33

$z = - \frac{9}{5}$

2.34

$r = - \frac{5}{16}$

2.35

$c = −3$

2.36

$x = - \frac{4}{7}$

2.37

$q = −6$

2.38

$r = −5$

2.39

$132 = −12 y; y = −11$

2.40

$117 = −13 z; z = −9$

2.41

$\frac{n}{7} = −21; n = −147$

2.42

$\frac{n}{8} = −56; n = −448$

2.43

$\frac{q}{−8} = 72; q = −576$

2.44

$\frac{p}{−9} = 81; p = −729$

2.45

$\frac{2}{5} f = 16; f = 40$

2.46

$\frac{3}{4} f = 21; f = 28$

2.47

$\frac{5}{8} + x = \frac{1}{4}; x = - \frac{3}{8}$

2.48

$\frac{3}{4} + x = \frac{5}{6}; x = \frac{1}{12}$

2.49

$0.39

2.50

$5.83

2.51

$120,000

2.52

21 flats

2.53

$x = −4$

2.54

$a = −8$

2.55

$y = 5$

2.56

$m = 9$

2.57

$n = −10$

2.58

$c = −1$

2.59

$p = −7$

2.60

$m = −3$

2.61

$j = 2$

2.62

$h = 1$

2.63

$x = −1$

2.64

$y = 4$

2.65

$q = 1$

2.66

$n = 1$

2.67

$a = −5$

2.68

$k = −6$

2.69

$x = 10$

2.70

$y = −3$

2.71

$x = −5$

2.72

$y = −5$

2.73

$x = 4$

2.74

$y = 1$

2.75

$y = −6$

2.76

$z = 8$

2.77

$m = 2$

2.78

$n = 2$

2.79

$u = 2$

2.80

$x = 4$

2.81

$j = \frac{5}{3}$

2.82

$k = \frac{5}{2}$

2.83

$p = −2$

2.84

$q = −8$

2.85

$y = - \frac{17}{5}$

2.86

$z = 0$

2.87

$n = 1$

2.88

$m = −1$

2.89

identity; all real numbers

2.90

identity; all real numbers

2.91

conditional equation; $q = \frac{9}{11}$

2.92

conditional equation; $k = \frac{193}{14}$

2.93

contradiction; no solution

2.94

contradiction; no solution

2.95

$x = \frac{1}{2}$

2.96

$x = −2$

2.97

$x = 12$

2.98

$u = −12$

2.99

$x = −1$

2.100

$c = −2$

2.101

$p = −4$

2.102

$q = 2$

2.103

$n = 2$

2.104

$m = −1$

2.105

$y = 2$

2.106

$z = −2$

2.107

$b = −20$

2.108

$c = −6$

2.109

$r = 1$

2.110

$s = −8$

2.111

$h = 12$

2.112

$k = −1$

2.113

$n = 9$

2.114

$d = 16$

2.115

330 miles

2.116

7 miles

2.117

11 hours

2.118

56 mph

2.119

ⓐ $r = 45$ ⓑ $r = \frac{d}{t}$

2.120

ⓐ $r = 65$ ⓑ $r = \frac{d}{t}$

2.121

ⓐ $h = 20$ ⓑ $h = \frac{2 A}{b}$

2.122

ⓐ $b = 4$ ⓑ $b = \frac{2 A}{h}$

2.123

ⓐ $12,000 ⓑ $P = \frac{I}{r t}$

2.124

ⓐ $9,000 ⓑ $P = \frac{I}{r t}$

2.125

ⓐ $y = 1$ ⓑ $y = \frac{10 - 3 x}{4}$

2.126

ⓐ $y = −1$ ⓑ $y = \frac{18 - 5 x}{2}$

2.127

$b = P - a - c$

2.128

$c = P - a - b$

2.129

$y = \frac{9 - 4 x}{7}$

2.130

$y = \frac{1 - 5 x}{8}$

2.131

ⓐ
ⓑ
ⓒ

2.132

ⓐ
ⓑ
ⓒ

2.133

ⓐ
ⓑ
ⓒ

2.134

ⓐ
ⓑ
ⓒ

2.135

2.136

2.137

$c > 8$

2.138

$(-∞, 5]$

2.139

$q > −4$

2.140

2.141

2.142

2.143

2.144

2.145

2.146

2.147

2.148

2.149

2.150

2.151

2.152

2.153

2.154

2.155

2.156

Section 2.1 Exercises

1.

yes

3.

no

5.

$x = 11$

7.

$y = −111$

9.

$b = \frac{1}{2}$

11.

$p = −11.7$

13.

$a = 121$

15.

$m = −182$

17.

$x = \frac{7}{3}$

19.

$y = 13.8$

21.

$x = −255$

23.

$z = −9.02$

25.

$q = - \frac{1}{4}$

27.

$p = \frac{16}{15}$

29.

$c = 25$

31.

$x = 1$

33.

$x = 0$

35.

$y = 8$ $y = 24$

37.

$u = −7.1$

39.

$a = −30$

41.

$y = 28$

43.

$n = −50$

45.

$j = 8$

47.

$a = - \frac{11}{4}$

49.

$x = 13$

51.

$x + 9 = 52; x = 43$

53.

$m - 10 = −14; m = −4$

55.

$y + (−30) = 40; y = 70$

57.

$9 x - 8 x = 107; 107$

59.

$n - \frac{1}{6} = \frac{1}{2}; \frac{2}{3}$

61.

$−4 n + 5 n = −82; - 82$

63.

11 miles

65.

7 years old

67.

21 pounds

69.

100.5 degrees

71.

$121.19

73.

$d = \frac{17}{24} inch$

75.

No. Justifications will vary.

Section 2.2 Exercises

77.

$x = 7$

79.

$c = −11$

81.

$y = - \frac{809}{15}$

83.

$p = - \frac{541}{37}$

85.

$z = 13$

87.

$x = 0$

89.

$x = 140$

91.

$q = 100$

93.

$y = −144$

95.

$m = −540$

97.

$y = −6$

99.

$v = 72$

101.

$y = 72$

103.

$w = −64$

105.

$a = −4$

107.

$x = \frac{20}{3}$

109.

$p = - \frac{7}{9}$

111.

$u = \frac{1}{4}$

113.

$p = −12$

115.

$n = 88$

117.

$d = 15$

119.

$q = −11$

121.

$x = - \frac{72}{5}$

123.

$x = 100$

125.

$y = 9$

127.

$w = −198$

129.

$a = \frac{9}{2}$

131.

$x = −2$

133.

$m = 27$

135.

$p = 2130$

137.

$y = −7$

139.

$c = 51$

141.

$x = 8$

143.

$133 = −19 n; n = −7$

145.

$−152 = 8 q; q = −19$

147.

$\frac{r}{12} = −48; r = −576$

149.

$\frac{j}{−20} = −80; j = 1,600$

151.

$\frac{b}{−6} = 18; b = −108$

153.

$\frac{k}{22} = −66; k = −1,452$

155.

$\frac{3}{10} x = 15; x = 50$

157.

$\frac{5}{2} v = 50; v = 20$

159.

$\frac{2}{5} + f = \frac{1}{2}; f = \frac{1}{10}$

161.

$q - \frac{1}{8} = \frac{3}{4}; q = \frac{7}{8}$

163.

6 balloons

165.

$1.08

167.

36 mpg

169.

$195,000

171.

15 49-cent stamps

173.

Answers will vary.

Section 2.3 Exercises

175.

$x = 6$

177.

$y = 6$

179.

$m = −8$

181.

$b = −8$

183.

$x = −4$

185.

$q = - \frac{9}{7}$

187.

$k = −11$

189.

$x = 9$

191.

$b = −3$

193.

$z = 3$

195.

$x = - \frac{3}{4}$

197.

$r = −2$

199.

$x = 19$

201.

$f = 7$

203.

$q = −5$

205.

$c = −4$

207.

$x = 2$

209.

$p = - \frac{8}{5}$

211.

$y = 4$

213.

$m = −6$

215.

$a = 7$

217.

$a = −40$

219.

$p = 15$

221.

$z = 3.46$

223.

$w = 60$

225.

$x = 23$

227.

30 feet

229.

$x = 2$ Justifications will vary.

231.

Yes. Justifications will vary.

Section 2.4 Exercises

233.

$y = 3$

235.

$n = −2$

237.

$p = - \frac{4}{3}$

239.

$t = −9$

241.

$b = 2$

243.

$m = 6$

245.

$k = \frac{3}{2}$

247.

$t = 1$

249.

$x = −2$

251.

$x = 5$

253.

$d = 1$

255.

$r = −7$

257.

$m = −15$

259.

$y = −4$

261.

$w = \frac{1}{2}$

263.

$a = 4$

265.

$r = 8$

267.

$m = 3$

269.

$y = −3$

271.

$x = 34$

273.

$x = −6$

275.

$n = −1$

277.

$a = −4$

279.

$m = −4$

281.

$d = −3$

283.

$k = \frac{3}{5}$

285.

$n = −5$

287.

$v = 1$

289.

$p = −34$

291.

$m = −4$

293.

identity; all real numbers

295.

identity; all real numbers

297.

conditional equation; $d = \frac{2}{3}$

299.

conditional equation; $n = 7$

301.

contradiction; no solution

303.

contradiction; no solution

305.

conditional equation; $k = 26$

307.

contradiction; no solution

309.

identity; all real numbers

311.

identity; all real numbers

313.

8 nickels

315.

Answers will vary.

317.

Answers will vary.

Section 2.5 Exercises

319.

$x = 1$

321.

$y = −1$

323.

$b = −2$

325.

$x = 3$

327.

$n = −24$

329.

$x = −4$

331.

$z = −2$

333.

$a = 1$

335.

$x = −6$

337.

$x = 1$

339.

$q = 7$

341.

$x = - \frac{5}{2}$

343.

$m = −1$

345.

$p = −4$

347.

$v = 20$

349.

$d = −24$

351.

$y = −1$

353.

$v = 4$

355.

$y = 15$

357.

$k = 2$

359.

$x = 20$

361.

$x = 22$

363.

$x = 8$

365.

$n = 19$

367.

$d = 10$

369.

$q = 15$

371.

$s = 35$

373.

Answers will vary.

375.

100. Justifications will vary.

Section 2.6 Exercises

377.

290 miles

379.

30 miles

381.

5 hours

383.

11.25 hours

385.

75 mph

387.

75 mph

389.

ⓐ $t = 4$ ⓑ $t = \frac{d}{r}$

391.

ⓐ $t = 3.5$ ⓑ $t = \frac{d}{r}$

393.

ⓐ $r = 70$ ⓑ $r = \frac{d}{t}$

395.

ⓐ $r = 40$ ⓑ $r = \frac{d}{t}$

397.

ⓐ $h = 16$ ⓑ $h = \frac{2 A}{b}$

399.

ⓐ $b = 10$ ⓑ $b = \frac{2 A}{h}$

401.

ⓐ $P = $ 13, 166.67$ ⓑ $P = \frac{I}{r t}$

403.

ⓐ $t = 2$ years ⓑ $t = \frac{I}{\Pr}$

405.

ⓐ $y = −5$ ⓑ $y = \frac{10 - 5 x}{2}$

407.

ⓐ $y = 17$ ⓑ $y = 5 - 4 x$

409.

$a = 90 - b$

411.

$c = 180 - a - b$

413.

$y = 13 - 9 x$

415.

$y = −1 + 5 x$

417.

$y = \frac{11 - 3 x}{4}$

419.

$y = 3 + x$

421.

$W = \frac{P - 2 L}{2}$

423.

$π = \frac{C}{d}$

425.

$H = \frac{V}{L W}$

427.

10°C

429.

Answers will vary.

Section 2.7 Exercises

431.

ⓐ
ⓑ
ⓒ

433.

ⓐ
ⓑ
ⓒ

435.

ⓐ
ⓑ
ⓒ

437.

ⓐ
ⓑ
ⓒ

439.

441.

443.

445.

447.

449.

451.

453.

455.

457.

459.

461.

463.

465.

467.

469.

471.

473.

475.

477.

479.

481.

483.

485.

487.

489.

491.

493.

495.

497.

499.

501.

503.

505.

$h \leq 77$

507.

$n \leq 8$

509.

Answers will vary.

511.

Answers will vary.

Review Exercises

513.

no

515.

yes

517.

$y = −8$

519.

$n = 1.5$

521.

$x = 5$

523.

$p = 18.8$

525.

$y = −25$

527.

$d = 12.1$

529.

$x = −8$

531.

$p = −28$

533.

$n - 4 = 13; n = 17$

535.

161 pounds

537.

$131.19

539.

$a = −5$

541.

$y = −4$

543.

$y = −300$

545.

$u = \frac{3}{2}$

547.

$c = 324$

549.

$y = \frac{11}{8}$

551.

$x = −1$

553.

$d = 3$

555.

$\frac{b}{9} = −27; b = −243$

557.

$s - \frac{1}{12} = \frac{1}{4}; s = \frac{1}{3}$

559.

$32

561.

$w = 7$

563.

$n = −4$

565.

$a = −7$

567.

$x = \frac{3}{8}$

569.

$n = −5$

571.

$c = 32$

573.

$p = \frac{13}{2}$

575.

$n = 12$

577.

$m = −14$

579.

$q = 18$

581.

$x = −1$

583.

$k = \frac{3}{4}$

585.

contradiction; no solution

587.

identity; all real numbers

589.

$x = 15$

591.

$k = 41$

593.

$y = −1$

595.

$u = −85$

597.

$d = −20$

599.

5 hours

601.

37.5 miles

603.

ⓐ $r = 82 mph$ ; ⓑ $r = \frac{D}{t}$

605.

ⓐ $h = 17$ ⓑ $h = \frac{2 A}{b}$

607.

ⓐ $y = \frac{14}{3}$ ⓑ $y = \frac{6 - 4 x}{3}$

609.

$H = \frac{V}{L W}$

611.

ⓐ
ⓑ
ⓒ

613.

ⓐ
ⓑ
ⓒ

615.

617.

619.

621.

623.

625.

627.

629.

Practice Test

631.

ⓐ no ⓑ yes

633.

$c = 32$

635.

$x = −5$

637.

$x = 9$

639.

$y = −4$

641.

$m = 9$

643.

$d = −14$

645.

$x = - \frac{1}{3}$

647.

$p = \frac{10}{3}$

649.

contradiction; no solution

651.

ⓐ $y = 4$ ⓑ $y = \frac{5 - x}{2}$

653.

655.

657.

$n + 15 \geq 48; n \geq 33$

659.

$120 = \frac{2}{3} p$ ; The original price was $180.