Chapter 2

Be Prepared

2.1

$1$

2.2

$20$

2.3

$n + 4$

2.4

$x - 5$

2.5

$1$

2.6

$- 25$

2.7

$4 y$

2.8

$- a + 4$

2.9

$18 x + 30$

2.10

$3 - 2 n$

2.11

$21 y + 27$

2.12

$16$

2.13

$3$

2.14

$12$

2.15

$478$

2.16

$8$

2.17

$12$

2.18

$15$ is greater than x.

2.19

$n = - 33$

2.20

$p = \frac{23}{5}$

2.21

$a = 2$

Try It

2.1

2.2

yes

2.3

$x = −46$

2.4

$x = −50$

2.5

$n = −14$

2.6

$p = −32$

2.7

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

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

$x - 12 = 51; x = 63$

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

$z = - \frac{9}{20}$

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; $k = \frac{201}{14}$

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

This figure shows the inequality p is greater than or equal to 11/12. Below this inequality is the inequality graphed on a number line ranging from 0 to 4, with tick marks at each integer. There is a bracket at p equals 11/12, and a dark line extends to the right from 11/12. Below the number line is the solution written in interval notation: bracket, 11/12 comma infinity, parenthesis.

2.136

This figure shows the inequality r is less than or equal to 11/12. Below this inequality is the inequality graphed on a number line ranging from 0 to 4, with tick marks at each integer. There is a bracket at r equals 11/12, and a dark line extends to the left from 11/12. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 11/12, bracket.

2.137

$c > 8$

2.138

$(-∞, 5]$

2.139

$q > −4$

2.140

2.141

This figure shows the inequality m is greater than or equal to 64. Below this inequality is a number line ranging from 63 to 67 with tick marks for each integer. The inequality m is greater than or equal to 64 is graphed on the number line, with an open bracket at m equals 64, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 64 comma infinity, parenthesis.

2.142

This figure shows the inequality n is greater than negative 18. Below this inequality is a number line ranging from negative 20 to negative 16 with tick marks for each integer. The inequality n is greater than negative 18 is graphed on the number line, with an open parenthesis at n equals negative 18, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 18 comma infinity, parenthesis.

2.143

This figure shows the inequality k is greater than or equal to negative 180. Below this inequality is a number line ranging from negative 181 to negative 177 with tick marks for each integer. The inequality k is greater than or equal to negative 180 is graphed on the number line, with an open bracket at n equals negative 180, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, negative 180 comma infinity, parenthesis.

2.144

This figure shows the inequality u is less than or equal to 64. Below this inequality is a number line ranging from 62 to 66 with tick marks for each integer. The inequality u is less than or equal to 64 is graphed on the number line, with an open bracket at u equals 64, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 64, bracket.

2.145

This figure shows the inequality q is less than or equal to 23/4. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality q is less than or equal to 23/4 is graphed on the number line, with an open bracket at q equals 23/4 (written in), and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 23/4, bracket.

2.146

This figure shows the inequality x is greater than negative 19/4. Below this inequality is a number line ranging from negative 7 to negative 3, with tick marks for each integer. The inequality x is greater than negative 19/4 is graphed on the number line, with an open parenthesis at x equals negative 19/4 (written in), and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 19/4 comma infinity, parenthesis.

2.147

This figure shows the inequality y is greater than negative 6. Below this inequality is a number line ranging from negative 7 to negative 3 with tick marks for each integer. The inequality y is greater than negative 6 is graphed on the number line, with an open parenthesis at y equals negative 6, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, negative 6 comma infinity, parenthesis.

2.148

This figure shows the inequality u is greater than 10. Below this inequality is a number line ranging from 9 to 13 with tick marks for each integer. The inequality u is greater than 10 is graphed on the number line, with an open parenthesis at u equals 10, and a dark line extending to the right of the parenthesis. The inequality is also written in interval notation as parenthesis, 10 comma infinity, parenthesis.

2.149

This figure shows an inequality that is an identity. Below this inequality is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. The inequality is also written in interval notation as parenthesis, negative infinity comma infinity, parenthesis.

2.150

2.151

This figure shows an inequality that is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. No inequality is graphed on the number line. Below the number line is the statement: “No solution.”

2.152

2.153

This figure shows the inequality 20y is less than or equal to 100, and then its solution: y is less than or equal to 5. Below this inequality is a number line ranging from 4 to 8 with tick marks for each integer. The inequality y is less than or equal to 5 is graphed on the number line, with an open bracket at y equals 5, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity comma 5, bracket.

2.154

This figure shows the inequality 9z is greater than or equal to 135, and then its solution: z is greater than or equal to 15. Below this inequality is a number line ranging from 14 to 18 with tick marks for each integer. The inequality z is greater than or equal to 15 is graphed on the number line, with an open bracket at z equals 15, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 15 comma infinity, parenthesis.

2.155

This figure shows the inequality p minus 19 is greater than or equal to 47, and then its solution: p is greater than or equal to 66. Below this inequality is a number line ranging from 65 to 69 with tick marks for each integer. The inequality p is greater than or equal to 66 is graphed on the number line, with an open bracket at p equals 66, and a dark line extending to the right of the bracket. The inequality is also written in interval notation as bracket, 66 comma infinity, parenthesis.

2.156

This figure shows the inequality a plus 4 is less than or equal to 15, and then its solution: a is less than or equal to 11. Below this inequality is a number line ranging from 10 to 14 with tick marks for each integer. The inequality a is less than or equal to 11 is graphed on the number line, with an open bracket at a equals 11, and a dark line extending to the left of the bracket. The inequality is also written in interval notation as parenthesis, negative infinity 11, bracket.

Section 2.1 Exercises

yes

$x = 11$

$y = −111$

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

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.

$y = 24$

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.

$d = \frac{13}{24} inch$

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.

$z = −7$

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.

$y = \frac{11 - 3 x}{2}$

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.

At the top of this figure is the solution to the inequality: m is less than or equal to 107. Below this is a number line ranging from 105 to 109 with tick marks for each integer. The inequality x is less than or equal to 107 is graphed on the number line, with an open bracket at x equals 107, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 107, bracket.

441.

At the top of this figure is the solution to the inequality: v is greater than negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality x is greater than negative 9 is graphed on the number line, with an open parenthesis at x equals negative 9, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 9 comma infinity, parenthesis.

443.

At the top of this figure is the solution to the inequality: b is greater than or equal to negative 17/24. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to negative 17/24 is graphed on the number line, with an open bracket at b equals negative 17/24 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 17/24 comma infinity, parenthesis.

445.

At the top of this figure is the solution to the inequality: g is less than 23/26. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality g is less than 23/26 is graphed on the number line, with an open parenthesis at g equals 23/26 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 23/26, parenthesis.

447.

At the top of this figure is the solution to the inequality: y is less than 8. Below this is a number line ranging from 6 to 10 with tick marks for each integer. The inequality y is less than 8 is graphed on the number line, with an open parenthesis at y equals 8, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 8, parenthesis.

449.

At the top of this figure is the solution to the inequality: s is greater than or equal to 9. Below this is a number line ranging from 7 to 11 with tick marks for each integer. The inequality s is greater than or equal to 9 is graphed on the number line, with an open bracket at s equals 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 9 comma infinity, parenthesis.

451.

At the top of this figure is the solution to the inequality: v is greater than or equal to negative 12. Below this is a number line ranging from negative 14 to negative 10 with tick marks for each integer. The inequality v is greater than or equal to negative 12 is graphed on the number line, with an open bracket at v equals negative 12, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 12 comma infinity, parenthesis.

453.

At the top of this figure is the solution to the inequality: d is less than negative 15. Below this is a number line ranging from negative 17 to negative 13 with tick marks for each integer. The inequality d is less than negative 15 is graphed on the number line, with an open parenthesis at d equals negative 15, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 15, parenthesis.

455.

At the top of this figure is the solution to the inequality: k is greater than 64. Below this is a number line ranging from 62 to 66 with tick marks for each integer. The inequality k is greater than 64 is graphed on the number line, with an open parenthesis at k equals 64, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 64, parenthesis.

457.

At the top of this figure is the solution to the inequality: g is less than or equal to 16. Below this is a number line ranging from 14 to 18 with tick marks for each integer. The inequality g is less than or equal to 16 is graphed on the number line, with an open bracket at g equals 16, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 16, bracket.

459.

At the top of this figure is the solution to the inequality: b is less than or equal to negative 300. Below this is a number line ranging from negative 302 to negative 298 with tick marks for each integer. The inequality b is less than or equal to negative 300 is graphed on the number line, with an open bracket at b equals negative 300, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 300, bracket.

461.

At the top of this figure is the solution to the inequality: q is greater than 108. Below this is a number line ranging from 106 to 110 with tick marks for each integer. The inequality q is greater than 108 is graphed on the number line, with an open parenthesis at q equals 108, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, 108 comma infinity, parenthesis.

463.

At the top of this figure is the solution to the inequality: s is less than negative 4. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality s is less than negative 4 is graphed on the number line, with an open parenthesis at s equals negative 4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 4, parenthesis.

465.

At the top of this figure is the solution to the inequality: x is less than or equal to negative 75. Below this is a number line ranging from negative 77 to negative 73 with tick marks for each integer. The inequality x is less than or equal to negative 75 is graphed on the number line, with an open bracket at x equals negative 75, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 75, bracket.

467.

At the top of this figure is the solution to the inequality: au is greater than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality u is greater than or equal to 7 is graphed on the number line, with an open bracket at u equals 7, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 7 comma infinity, parenthesis.

469.

At the top of this figure is the solution to the inequality: p is less than 18/5. Below this is a number line ranging from 2 to 6 with tick marks for each integer. The inequality p is less than 18/5 is graphed on the number line, with an open parenthesis at p equals 18/5 (written in), and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 18/5, parenthesis.

471.

At the top of this figure is the solution to the inequality: y is less than negative 5. Below this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality y is less than negative 5 is graphed on the number line, with an open parenthesis at y equals negative 5, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 5, parenthesis.

473.

At the top of this figure is the solution to the inequality: x is less than or equal to 7. Below this is a number line ranging from 5 to 9 with tick marks for each integer. The inequality x is less than or equal to 7 is graphed on the number line, with an open bracket at x equals 7, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 7, bracket.

475.

At the top of this figure is the solution to the inequality: the inequality is an identity. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The identity is graphed on the number line, with a dark line extending in both directions. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma infinity, parenthesis.

477.

At the top of this figure is the result of the inequality: the inequality is a contradiction. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. Because this is a contradiction, no inequality is graphed on the number line. Below the number line is the statement: “No solution”.

479.

481.

483.

At the top of this figure is the solution to the inequality: k is greater than or equal to negative 11/5. Below this is a number line ranging from negative 4 to 0 with tick marks for each integer. The inequality k is greater than or equal to negative 11/5 is graphed on the number line, with an open bracket at k equals negative 11/5 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 11/5 comma infinity, parenthesis.

485.

487.

At the top of this figure is the solution to the inequality: y is greater than or equal to 10/49. Below this is a number line ranging from negative 1 to 3 with tick marks for each integer. The inequality y is greater than or equal to 10/49 is graphed on the number line, with an open bracket at y equals 10/49 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 10/49 comma infinity, parenthesis.

489.

At the top of this figure is the solution to the inequality: d is greater than negative 90. Below this is a number line ranging from negative 92 to negative 88 with tick marks for each integer. The inequality d is greater than negative 90 is graphed on the number line, with an open parenthesis at d equals negative 90, and a dark line extending to the right of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative 90 comma infinity, parenthesis.

491.

At the top of this figure is the solution to the inequality: n is less than or equal to negative 78. Below this is a number line ranging from negative 80 to negative 76 with tick marks for each integer. The inequality n is less than or equal to negative 78 is graphed on the number line, with an open bracket at n equals negative 78, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 78, bracket.

493.

At the top of this figure is the the inequality 90c is less than 450. Below this is the solution to the inequality: c is less than 5. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma 5, parenthesis. Below the interval notation is a number line ranging from 3 to 7 with tick marks for each integer. The inequality c is less than 5 is graphed on the number line, with an open parenthesis at c equals 5, and a dark line extending to the left of the parenthesis.

495.

At the top of this figure is the the inequality 10y is less than or equal to negative 110. Below this is the solution to the inequality: y is less than or equal to negative 11. Below the solution is the solution written in interval notation: parenthesis, negative infinity comma negative 11, bracket. Below the interval notation is a number line ranging from negative 13 to negative 9 with tick marks for each integer. The inequality y is less than or equal to negative 11 is graphed on the number line, with an open bracket at y equals negative 11, and a dark line extending to the left of the bracket.

497.

At the top of this figure is the the inequality k plus 6 is greater than 25. Below this is the solution to the inequality: k is greater than 19. Below the the solution written in interval notation: parenthesis, 19 comma infinity, parenthesis. Below the interval notation is a number line ranging from 17 to 21 with tick marks for each integer. The inequality k is greater than 19 is graphed on the number line, with an open parenthesis at k equals 19, and a dark line extending to the right of the parenthesis.

499.

At the top of this figure is the the inequality x minus 12 is greater than or equal to 21. Below this is the solution to the inequality: x is greater than or equal to 33. Below the solution is the solution written in interval notation: bracket, 33 comma infinity, parenthesis. Below the interval notation is a number line ranging from 32 to 36 with tick marks for each integer. The inequality x is greater than or equal to 33 is graphed on the number line, with an open bracket at x equals 33, and a dark line extending to the right of the bracket.

501.

At the top of this figure is the the inequality negative 2s is less than 56. Below this is the solution to the inequality: s is greater than negative 28. Below the solution is the solution written in interval notation: parenthesis, negative 28 comma infinity, parenthesis. Below the interval notation is a number line ranging from negative 30 to negative 26 with tick marks for each integer. The inequality s is greater than negative 28 is graphed on the number line, with an open parenthesis at s equals negative 28, and a dark line extending to the right of the parenthesis.

503.

At the top of this figure is the the inequality a minus 15 is greater than or equal to negative 7. Below this is the solution to the inequality: a is greater than or equal to 8. Below the solution is the solution written in interval notation: bracket, 8 comma infinity, parenthesis. Below the interval notation is a number line ranging from 0 to 10 with tick marks for each integer. The inequality a is greater than or equal to 8 is graphed on the number line, with an open bracket at a equals 8, and a dark line extending to the right of the bracket.

505.

$h \leq 77$

507.

$n \leq 8$

509.

Answers will vary.

511.

Answers will vary.

Review Exercises

513.

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.

$y = 47$

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.

At the top of this figure is the solution to the inequality: m is less than or equal to 42. Below this is a number line ranging from 40 to 44 with tick marks for each integer. The inequality m is less than or equal to 42 is graphed on the number line, with an open bracket at m equals 42, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 42, bracket

617.

At the top of this figure is the solution to the inequality: b is greater than or equal to 3/8. Below this is a number line ranging from negative 2 to 2 with tick marks for each integer. The inequality b is greater than or equal to 3/8 is graphed on the number line, with an open bracket at b equals 3/8 (written in), and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 3/8 comma infinity, bracket

619.

At the top of this figure is the solution to the inequality: d is greater than or equal to negative 9. Below this is a number line ranging from negative 11 to negative 7 with tick marks for each integer. The inequality d is greater than or equal to negative 9 is graphed on the number line, with an open bracket at d equals negative 9, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, negative 9 comma infinity, parenthesis.

621.

At the top of this figure is the solution to the inequality: q is less than or equal to 48. Below this is a number line ranging from 46 to 50 with tick marks for each integer. The inequality q is less than or equal to 48 is graphed on the number line, with an open bracket at q equals 48, and a dark line extending to the left of the bracket. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 48, bracket.

623.

At the top of this figure is the solution to the inequality: h is greater than or equal to 15. Below this is a number line ranging from 13 to 17 with tick marks for each integer. The inequality h is greater than or equal to 15 is graphed on the number line, with an open bracket at h equals 15, and a dark line extending to the right of the bracket. Below the number line is the solution written in interval notation: bracket, 15 comma infinity, parenthesis.

625.

At the top of this figure is the solution to the inequality: a is less than negative 6. Below this is a number line ranging from negative 8 to negative 4 with tick marks for each integer. The inequality a is less than negative 6 is graphed on the number line, with an open parenthesis at a equals negative 6, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma negative 6, parenthesis.

627.

At the top of this figure is the inequality c minus 3 is greater than or equal to 360. To the right of this is the solution to the inequality: c is greater than or equal to 363. To the right of the solution is the solution written in interval notation: bracket, 363 comma infinity, parenthesis. Below all of this is a number line ranging from 361 to 365 with tick marks for each integer. The inequality c is greater than or equal to 363 is graphed on the number line, with an open bracket at c equals 363, and a dark line extending to the right of the bracket.

629.

At the top of this figure is the inequality negative 2a is less than or equal to 8. To the right of this is the solution to the inequality: a is greater than or equal to negative 4. To the right of the solution is the solution written in interval notation: bracket, negative 4 comma infinity, parenthesis. Below all of this is a number line ranging from negative 6 to negative 2 with tick marks for each integer. The inequality a is greater than or equal to negative 4 is graphed on the number line, with an open bracket at a equals negative 4, and a dark line extending to the right of the bracket.

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.

This figure is a number line ranging from 1 to 5 with tick marks for each integer. The inequality x is less than 11/4 is graphed on the number line, with an open parenthesis at x equals 11/4, and a dark line extending to the left of the parenthesis. Below the number line is the solution written in interval notation: parenthesis, negative infinity comma 11/4, parenthesis.

655.

This figure is a number line ranging from negative 2 to 3 with tick marks for each integer. The inequality c is greater than 1/3 is graphed on the number line, with an open parenthesis at c equals 1/3, and a dark line extending to the right of the parenthesis. Below the number line is the solution: c is greater than 1/3. To the right of the solution is the solution written in interval notation: parenthesis, 1/3 comma infinity, parenthesis

657.

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

659.

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