Elementary Algebra

# Chapter 2

Elementary AlgebraChapter 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

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

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

$y − 12 = 51 ; y = 63 y − 12 = 51 ; y = 63$

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

$z = − 9 5 z = − 9 5$

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; $k=19314k=19314$ 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. 2.135 2.136 2.137 $c>8c>8$ 2.138 $(-∞,5](-∞,5]$ 2.139 $q > −4 q > −4$ 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. $x = 11 x = 11$ 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. $y = 8 y = 8$ $y = 24 y = 24$ 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.

$d = 17 24 inch d = 17 24 inch$

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.

$y = −7 y = −7$

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.

### 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.

303.

305.

conditional equation; $k=26k=26$

307.

309.

identity; all real numbers

311.

identity; all real numbers

313.

8 nickels

315.

317.

### 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.

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.

$y = 11 − 3 x 4 y = 11 − 3 x 4$

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.

### 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.

511.

### 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.

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.

$d = −20 d = −20$

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.

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. Do you know how you learn best?
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