Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Elementary Algebra 2e

Chapter 2

Elementary Algebra 2eChapter 2
Search for key terms or text.

Be Prepared

2.1

1 1

2.2

20 20

2.3

n + 4 n + 4

2.4

x − 5 x − 5

2.5

1 1

2.6

− 25 − 25

2.7

4 y 4 y

2.8

− a + 4 − a + 4

2.9

18 x + 30 18 x + 30

2.10

3 − 2 n 3 − 2 n

2.11

21 y + 27 21 y + 27

2.12

16 16

2.13

3 3

2.14

12 12

2.15

478 478

2.16

8 8

2.17

12 12

2.18

1515 is greater than x.

2.19

n = − 33 n = − 33

2.20

p = 23 5 p = 23 5

2.21

a = 2 a = 2

Try It

2.1

no

2.2

yes

2.3

x = −46 x = −46

2.4

x = −50 x = −50

2.5

n = −14 n = −14

2.6

p = −32 p = −32

2.7

p = 9 6 = 3 2 p = 9 6 = 3 2

2.8

q = 4 3 q = 4 3

2.9

b = −1.63 b = −1.63

2.10

c = −3.67 c = −3.67

2.11

y = 15 y = 15

2.12

z = 2 z = 2

2.13

p = 5 p = 5

2.14

q = −16 q = −16

2.15

h = 6 h = 6

2.16

x = 2 x = 2

2.17

x + 10 = 41 ; x = 31 x + 10 = 41 ; x = 31

2.18

x − 12 = 51 ; x = 63 x − 12 = 51 ; x = 63

2.19

4 x − 3 x = 14 ; x = 14 4 x − 3 x = 14 ; x = 14

2.20

7 a − 6 a = −8 ; a = −8 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 = −41 3 y = −41 3

2.26

z = −55 4 z = −55 4

2.27

a = 294 a = 294

2.28

b = 144 b = 144

2.29

k = −8 k = −8

2.30

g = −3 g = −3

2.31

n = 35 n = 35

2.32

y = 18 y = 18

2.33

z = − 9 20 z = − 9 20

2.34

r = − 5 16 r = − 5 16

2.35

c = −3 c = −3

2.36

x = − 4 7 x = − 4 7

2.37

q = −6 q = −6

2.38

r = −5 r = −5

2.39

132 = −12 y ; y = −11 132 = −12 y ; y = −11

2.40

117 = −13 z ; z = −9 117 = −13 z ; z = −9

2.41

n 7 = −21 ; n = −147 n 7 = −21 ; n = −147

2.42

n 8 = −56 ; n = −448 n 8 = −56 ; n = −448

2.43

q −8 = 72 ; q = −576 q −8 = 72 ; q = −576

2.44

p −9 = 81 ; p = −729 p −9 = 81 ; p = −729

2.45

2 5 f = 16 ; f = 40 2 5 f = 16 ; f = 40

2.46

3 4 f = 21 ; f = 28 3 4 f = 21 ; f = 28

2.47

5 8 + x = 1 4 ; x = − 3 8 5 8 + x = 1 4 ; x = − 3 8

2.48

3 4 + x = 5 6 ; x = 1 12 3 4 + x = 5 6 ; x = 1 12

2.49

$0.39

2.50

$5.83

2.51

$120,000

2.52

21 flats

2.53

x = −4 x = −4

2.54

a = −8 a = −8

2.55

y = 5 y = 5

2.56

m = 9 m = 9

2.57

n = −10 n = −10

2.58

c = −1 c = −1

2.59

p = −7 p = −7

2.60

m = −3 m = −3

2.61

j = 2 j = 2

2.62

h = 1 h = 1

2.63

x = −1 x = −1

2.64

y = 4 y = 4

2.65

q = 1 q = 1

2.66

n = 1 n = 1

2.67

a = −5 a = −5

2.68

k = −6 k = −6

2.69

x = 10 x = 10

2.70

y = −3 y = −3

2.71

x = −5 x = −5

2.72

y = −5 y = −5

2.73

x = 4 x = 4

2.74

y = 1 y = 1

2.75

y = −6 y = −6

2.76

z = 8 z = 8

2.77

m = 2 m = 2

2.78

n = 2 n = 2

2.79

u = 2 u = 2

2.80

x = 4 x = 4

2.81

j = 5 3 j = 5 3

2.82

k = 5 2 k = 5 2

2.83

p = −2 p = −2

2.84

q = −8 q = −8

2.85

y = − 17 5 y = − 17 5

2.86

z = 0 z = 0

2.87

n = 1 n = 1

2.88

m = −1 m = −1

2.89

identity; all real numbers

2.90

identity; all real numbers

2.91

conditional equation; q=–911q=–911

2.92

conditional equation; k=20114k=20114

2.93

contradiction; no solution

2.94

contradiction; no solution

2.95

x = 1 2 x = 1 2

2.96

x = −2 x = −2

2.97

x = 12 x = 12

2.98

u = −12 u = −12

2.99

x = −1 x = −1

2.100

c = −2 c = −2

2.101

p = −4 p = −4

2.102

q = 2 q = 2

2.103

n = 2 n = 2

2.104

m = −1 m = −1

2.105

y = 2 y = 2

2.106

z = −2 z = −2

2.107

b = −20 b = −20

2.108

c = −6 c = −6

2.109

r = 1 r = 1

2.110

s = −8 s = −8

2.111

h = 12 h = 12

2.112

k = −1 k = −1

2.113

n = 9 n = 9

2.114

d = 16 d = 16

2.115

330 miles

2.116

7 miles

2.117

11 hours

2.118

56 mph

2.119

ⓐ r=45r=45 ⓑ r=dtr=dt

2.120

ⓐ r=65r=65 ⓑ r=dtr=dt

2.121

ⓐ h=20h=20 ⓑ h=2Abh=2Ab

2.122

ⓐ b=4b=4 ⓑ b=2Ahb=2Ah

2.123

ⓐ $12,000 ⓑ P=IrtP=Irt

2.124

ⓐ $9,000 ⓑ P=IrtP=Irt

2.125

ⓐ y=−1y=−1 ⓑ y=10−3x4y=10−3x4

2.126

ⓐ y=−1y=−1 ⓑ y=18−5x2y=18−5x2

2.127

b = P − a − c b = P − a − c

2.128

c = P − a − b c = P − a − b

2.129

y = 9 − 4 x 7 y = 9 − 4 x 7

2.130

y = 1 − 5 x 8 y = 1 − 5 x 8

2.131
  1. ⓐ
  2. ⓑ
  3. ⓒ
2.132
  1. ⓐ
  2. ⓑ
  3. ⓒ
2.133
  1. ⓐ
  2. ⓑ
  3. ⓒ
2.134
  1. ⓐ
  2. ⓑ
  3. ⓒ
2.137

c>8c>8

2.138

(-∞,5](-∞,5]

2.139

q > −4 q > −4

Section 2.1 Exercises

1.

yes

3.

no

5.

x = 11 x = 11

7.

y = −111 y = −111

9.

b = 1 2 b = 1 2

11.

p = −11.7 p = −11.7

13.

a = 121 a = 121

15.

m = −182 m = −182

17.

x = 7 3 x = 7 3

19.

y = 13.8 y = 13.8

21.

x = −255 x = −255

23.

z = −9.02 z = −9.02

25.

q = − 1 4 q = − 1 4

27.

p = 16 15 p = 16 15

29.

c = 25 c = 25

31.

x = 1 x = 1

33.

x = 0 x = 0

35.

y = 24 y = 24

37.

u = −7.1 u = −7.1

39.

a = −30 a = −30

41.

y = 28 y = 28

43.

n = −50 n = −50

45.

j = 8 j = 8

47.

a = − 11 4 a = − 11 4

49.

x = 13 x = 13

51.

x + 9 = 52 ; x = 43 x + 9 = 52 ; x = 43

53.

m − 10 = −14 ; m = −4 m − 10 = −14 ; m = −4

55.

y + ( −30 ) = 40 ; y = 70 y + ( −30 ) = 40 ; y = 70

57.

9 x − 8 x = 107 ; 107 9 x − 8 x = 107 ; 107

59.

n − 1 6 = 1 2 ; 2 3 n − 1 6 = 1 2 ; 2 3

61.

−4 n + 5 n = −82 ; − 82 −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 = 13 24 inch d = 13 24 inch

75.

No. Justifications will vary.

Section 2.2 Exercises

77.

x = 7 x = 7

79.

c = −11 c = −11

81.

y = − 809 15 y = − 809 15

83.

p = 541 37 p = 541 37

85.

z = 13 z = 13

87.

x = 0 x = 0

89.

x = 140 x = 140

91.

q = 100 q = 100

93.

y = −144 y = −144

95.

m = −540 m = −540

97.

y = −6 y = −6

99.

v = 72 v = 72

101.

y = 72 y = 72

103.

w = −64 w = −64

105.

a = −4 a = −4

107.

x = 20 3 x = 20 3

109.

p = − 7 9 p = − 7 9

111.

u = 1 4 u = 1 4

113.

p = −12 p = −12

115.

n = 88 n = 88

117.

d = 15 d = 15

119.

q = −11 q = −11

121.

x = − 72 5 x = − 72 5

123.

x = 100 x = 100

125.

y = 9 y = 9

127.

w = −198 w = −198

129.

a = 9 2 a = 9 2

131.

x = −2 x = −2

133.

m = 27 m = 27

135.

p = 2130 p = 2130

137.

z = −7 z = −7

139.

c = 51 c = 51

141.

x = 8 x = 8

143.

133 = −19 n ; n = −7 133 = −19 n ; n = −7

145.

−152 = 8 q ; q = −19 −152 = 8 q ; q = −19

147.

r 12 = −48 ; r = −576 r 12 = −48 ; r = −576

149.

j −20 = −80 ; j = 1,600 j −20 = −80 ; j = 1,600

151.

b −6 = 18 ; b = −108 b −6 = 18 ; b = −108

153.

k 22 = −66 ; k = −1,452 k 22 = −66 ; k = −1,452

155.

3 10 x = 15 ; x = 50 3 10 x = 15 ; x = 50

157.

5 2 v = 50 ; v = 20 5 2 v = 50 ; v = 20

159.

2 5 + f = 1 2 ; f = 1 10 2 5 + f = 1 2 ; f = 1 10

161.

q − 1 8 = 3 4 ; q = 7 8 q − 1 8 = 3 4 ; q = 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 x = 6

177.

y = 6 y = 6

179.

m = −8 m = −8

181.

b = −8 b = −8

183.

x = −4 x = −4

185.

q = − 9 7 q = − 9 7

187.

k = −11 k = −11

189.

x = 9 x = 9

191.

b = −3 b = −3

193.

z = 3 z = 3

195.

x = − 3 4 x = − 3 4

197.

r = −2 r = −2

199.

x = 19 x = 19

201.

f = 7 f = 7

203.

q = −5 q = −5

205.

c = −4 c = −4

207.

x = 2 x = 2

209.

p = − 8 5 p = − 8 5

211.

y = 4 y = 4

213.

m = −6 m = −6

215.

a = 7 a = 7

217.

a = −40 a = −40

219.

p = 15 p = 15

221.

z = 3.46 z = 3.46

223.

w = 60 w = 60

225.

x = 23 x = 23

227.

30 feet

229.

x=2x=2 Justifications will vary.

231.

Yes. Justifications will vary.

Section 2.4 Exercises

233.

y = 3 y = 3

235.

n = −2 n = −2

237.

p = − 4 3 p = − 4 3

239.

t = −9 t = −9

241.

b = 2 b = 2

243.

m = 6 m = 6

245.

k = 3 2 k = 3 2

247.

t = 1 t = 1

249.

x = −2 x = −2

251.

x = 5 x = 5

253.

d = 1 d = 1

255.

r = −7 r = −7

257.

m = −15 m = −15

259.

y = −4 y = −4

261.

w = 1 2 w = 1 2

263.

a = 4 a = 4

265.

r = 8 r = 8

267.

m = 3 m = 3

269.

y = −3 y = −3

271.

x = 34 x = 34

273.

x = −6 x = −6

275.

n = −1 n = −1

277.

a = −4 a = −4

279.

m = −4 m = −4

281.

d = −3 d = −3

283.

k = 3 5 k = 3 5

285.

n = −5 n = −5

287.

v = 1 v = 1

289.

p = −34 p = −34

291.

m = −4 m = −4

293.

identity; all real numbers

295.

identity; all real numbers

297.

conditional equation; d=23d=23

299.

conditional equation; n=7n=7

301.

contradiction; no solution

303.

contradiction; no solution

305.

conditional equation; k=26k=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 x = 1

321.

y = −1 y = −1

323.

b = −2 b = −2

325.

x = 3 x = 3

327.

n = −24 n = −24

329.

x = −4 x = −4

331.

z = −2 z = −2

333.

a = 1 a = 1

335.

x = −6 x = −6

337.

x = 1 x = 1

339.

q = 7 q = 7

341.

x = − 5 2 x = − 5 2

343.

m = −1 m = −1

345.

p = −4 p = −4

347.

v = 20 v = 20

349.

d = −24 d = −24

351.

y = −1 y = −1

353.

v = 4 v = 4

355.

y = 15 y = 15

357.

k = 2 k = 2

359.

x = 20 x = 20

361.

x = 22 x = 22

363.

x = 8 x = 8

365.

n = 19 n = 19

367.

d = 10 d = 10

369.

q = 15 q = 15

371.

s = 35 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=4t=4 ⓑ t=drt=dr

391.

ⓐ t=3.5t=3.5 ⓑ t=drt=dr

393.

ⓐ r=70r=70 ⓑ r=dtr=dt

395.

ⓐ r=40r=40 ⓑ r=dtr=dt

397.

ⓐ h=16h=16 ⓑ h=2Abh=2Ab

399.

ⓐ b=10b=10 ⓑ b=2Ahb=2Ah

401.

ⓐ P=$13,166.67P=$13,166.67 ⓑ P=IrtP=Irt

403.

ⓐ t=2t=2 years ⓑ t=IPrt=IPr

405.

ⓐ y=−5y=−5 ⓑ y=10−5x2y=10−5x2

407.

ⓐ y=17y=17 ⓑ y=5−4xy=5−4x

409.

a = 90 − b a = 90 − b

411.

c = 180 − a − b c = 180 − a − b

413.

y = 13 − 9 x y = 13 − 9 x

415.

y = −1 + 5 x y = −1 + 5 x

417.

y = 11 − 3 x 2 y = 11 − 3 x 2

419.

y = 3 + x y = 3 + x

421.

W = P − 2 L 2 W = P − 2 L 2

423.

π = C d π = C d

425.

H = V L W H = V L W

427.

10°C

429.

Answers will vary.

Section 2.7 Exercises

431.
  1. ⓐ
  2. ⓑ
  3. ⓒ
433.
  1. ⓐ
  2. ⓑ
  3. ⓒ
435.
  1. ⓐ
  2. ⓑ
  3. ⓒ
437.
  1. ⓐ
  2. ⓑ
  3. ⓒ
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 ≤ 77 h ≤ 77

507.

n ≤ 8 n ≤ 8

509.

Answers will vary.

511.

Answers will vary.

Review Exercises

513.

no

515.

yes

517.

y = −8 y = −8

519.

n = 1.5 n = 1.5

521.

x = 5 x = 5

523.

p = 18.8 p = 18.8

525.

y = −25 y = −25

527.

d = 12.1 d = 12.1

529.

x = −8 x = −8

531.

p = −28 p = −28

533.

n − 4 = 13 ; n = 17 n − 4 = 13 ; n = 17

535.

161 pounds

537.

$131.19

539.

a = −5 a = −5

541.

y = −4 y = −4

543.

y = −300 y = −300

545.

u = 3 2 u = 3 2

547.

c = 324 c = 324

549.

y = 11 8 y = 11 8

551.

x = −1 x = −1

553.

d = 3 d = 3

555.

b 9 = −27 ; b = −243 b 9 = −27 ; b = −243

557.

s − 1 12 = 1 4 ; s = 1 3 s − 1 12 = 1 4 ; s = 1 3

559.

$32

561.

w = 7 w = 7

563.

n = −4 n = −4

565.

a = −7 a = −7

567.

x = 3 8 x = 3 8

569.

n = −5 n = −5

571.

c = 32 c = 32

573.

p = 13 2 p = 13 2

575.

n = 12 n = 12

577.

m = −14 m = −14

579.

q = 18 q = 18

581.

x = −1 x = −1

583.

k = 3 4 k = 3 4

585.

contradiction; no solution

587.

identity; all real numbers

589.

x = 15 x = 15

591.

k = 41 k = 41

593.

y = −1 y = −1

595.

u = −85 u = −85

597.

y = 47 y = 47

599.

5 hours

601.

37.5 miles

603.

ⓐ r=82mphr=82mph; ⓑ r=Dtr=Dt

605.

ⓐ h=17h=17 ⓑ h=2Abh=2Ab

607.

ⓐ y=143y=143 ⓑ y=6−4x3y=6−4x3

609.

H = V L W H = V L W

611.
  1. ⓐ
  2. ⓑ
  3. ⓒ
613.
  1. ⓐ
  2. ⓑ
  3. ⓒ
615.
617.
619.
621.
623.
625.
627.
629.

Practice Test

631.

ⓐ no ⓑ yes

633.

c = 32 c = 32

635.

x = −5 x = −5

637.

x = 9 x = 9

639.

y = −4 y = −4

641.

m = 9 m = 9

643.

d = −14 d = −14

645.

x = − 1 3 x = − 1 3

647.

p = 10 3 p = 10 3

649.

contradiction; no solution

651.

ⓐ y=4y=4 ⓑ y=5−x2y=5−x2

653.
655.
657.

n + 15 ≥ 48 ; n ≥ 33 n + 15 ≥ 48 ; n ≥ 33

659.

120=23p120=23p; The original price was $180.

PreviousNext
Order a print copy
Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/elementary-algebra-2e/pages/1-introduction

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/elementary-algebra-2e/pages/1-introduction

Citation information

© Jul 8, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.