Elementary Algebra 2e

# Chapter 1

### Try It

1.1

ten millions tens hundred thousands millions ones

1.2

billions ten thousands tens hundred thousands hundred millions

1.3

nine trillion, two hundred fifty-eight billion, one hundred thirty-seven million, nine hundred four thousand, sixty-one

1.4

seventeen trillion, eight hundred sixty-four billion, three hundred twenty-five million, six hundred nineteen thousand four

1.5

$2,466,714,0512,466,714,051$

1.6

$11,921,830,10611,921,830,106$

1.7

$17,90017,900$

1.8

$468,800468,800$

1.9

207,000 207,000 210,000

1.10

785,000 785,000 780,000

1.11

by 2, 3, and 6

1.12

by 3 and 5

1.13

$2·2·2·2·52·2·2·2·5$

1.14

$2·2·3·52·2·3·5$

1.15

$2·3·3·72·3·3·7$

1.16

$2·3·7·72·3·7·7$

1.17

36

1.18

72

1.19

36

1.20

72

1.21

84

1.22

96

1.23

14 is less than or equal to 27 19 minus 2 is not equal to 8 12 is greater than 4 divided by 2 x minus 7 is less than 1

1.24

19 is greater than or equal to 15 7 is equal to 12 minus 5 15 divided by 3 is less than 8 y plus 3 is greater than 6

1.25

equation expression

1.26

expression equation

1.27

125 1

1.28

49 0

1.29

2 14

1.30

35 99

1.31

16

1.32

23

1.33

86

1.34

1

1.35

13 5

1.36

8 16

1.37

$99$ $6464$

1.38

$216216$ $6464$

1.39

40

1.40

9

1.41

17 41 1

1.42

9 13 1

1.43

9 and 15, $y2y2$ and $11y2,11y2,$ $2x32x3$ and $8x38x3$

1.44

19 and 24, $8x28x2$ and $3x2,3x2,$ $4x34x3$ and $6x36x3$

1.45

$4x2,5x,174x2,5x,17$

1.46

5x, 2y

1.47

$10x2+16x+1710x2+16x+17$

1.48

$12y2+9y+712y2+9y+7$

1.49

$14x2−1314x2−13$ $12x÷212x÷2$

1.50

$17y2+1917y2+19$ 7y

1.51

$x+11x+11$ $11a−1411a−14$

1.52

$z+13z+13$ $8x−188x−18$

1.53

$4(p+q)4(p+q)$ $4p+q4p+q$

1.54

$2x−82x−8$ $2(x−8)2(x−8)$

1.55

$w−7w−7$

1.56

$l−6l−6$

1.57

$4q−84q−8$

1.58

$7n+37n+3$

1.59

> < > >

1.60

< > < >

1.61

$−4−4$ 3 1

1.62

$−8−8$ 5 5

1.63

$−4−4$ 4

1.64

$−11−11$ 11

1.65

4 28 0

1.66

13 47 0

1.67

> > < >

1.68

> > > <

1.69

16

1.70

9

1.71

$1717$ $3939$ $−22−22$ $−11−11$

1.72

$2323$ $2121$ $−37−37$ $−49−49$

1.73

6 $−6−6$

1.74

7 $−7−7$

1.75

2 $−2−2$

1.76

3 $−3−3$

1.77

$−50−50$ $−17−17$

1.78

$−70−70$ $−36−36$

1.79

13

1.80

0

1.81

2 $−2−2$

1.82

3 $−3−3$

1.83

$−10−10$ 10

1.84

$−11−11$ 11

1.85

8 −18

1.86

$88$ $−22−22$

1.87

$1919$ $−4−4$

1.88

23 3

1.89

3

1.90

13

1.91

$−48−48$ 28 $−63−63$ 60

1.92

$−56−56$ 54 $−28−28$ 39

1.93

$−9−9$ 17

1.94

$−8−8$ 16

1.95

$−7−7$ 39

1.96

$−9−9$ 23

1.97

$−63−63$

1.98

$−84−84$

1.99

81 $−81−81$

1.100

49 $−49−49$

1.101

29

1.102

52

1.105

21

1.107

$−6−6$ 10

1.108

$−1−1$ 17

1.109

196

1.111

$−2−2$ 36

1.112

$−19−19$ 9

1.113

39

1.114

13

1.115

$(9+(−16))+4;−3(9+(−16))+4;−3$

1.116

$(−8+(−12))+7;−13(−8+(−12))+7;−13$

1.117

$14−(−23);3714−(−23);37$ $−17−21;−38−17−21;−38$

1.118

$11−(−19);3011−(−19);30$ $−11−18;−29−11−18;−29$

1.119

$−5(12);−60−5(12);−60$

1.120

$8(−13);−1048(−13);−104$

1.121

$−63÷(−9);7−63÷(−9);7$

1.122

$−72÷(−9);8−72÷(−9);8$

1.123

The difference in temperatures was 45 degrees.

1.124

The difference in temperatures was 9 degrees.

1.125

The Bears lost 105 yards.

1.126

A $16 fee was deducted from his checking account. 1.127 $610,915,1220;610,915,1220;$ answers may vary 1.128 $810,1215,1620;810,1215,1620;$ answers may vary 1.129 $−79−79$ 1.130 $−59−59$ 1.131 $−2340−2340$ 1.132 $−58−58$ 1.133 $xyxy$ 1.134 $abab$ 1.135 $−421−421$ 1.136 $−316−316$ 1.137 $−33a−33a$ 1.138 $−26b−26b$ 1.139 $−215p−215p$ 1.140 $−158q−158q$ 1.141 $415415$ 1.142 $2323$ 1.143 $4545$ 1.144 $11141114$ 1.145 $34b34b$ 1.146 $4q4q$ 1.147 $−34−34$ 1.148 $−53−53$ 1.151 $a−bcda−bcd$ 1.152 $p+qrp+qr$ 1.153 $x+34x+34$ 1.154 $y+58y+58$ 1.155 $−1314−1314$ 1.156 $−78−78$ 1.157 $−16x−16x$ 1.158 $−22a−22a$ 1.159 $−1−1$ 1.160 $−23−23$ 1.161 $79607960$ 1.162 $1036010360$ 1.163 $196196$ 1.164 $7522475224$ 1.165 $3y+14183y+1418$ 1.166 $5x+14305x+1430$ 1.167 $27a−323627a−3236$ $2a32a3$ 1.168 $24k−53024k−530$ $2k152k15$ 1.169 $190190$ 1.170 $272272$ 1.172 $2727$ 1.173 $−1−1$ $−12−12$ 1.174 $7676$ $−14−14$ 1.175 $−14−14$ 1.176 $−178−178$ 1.177 $−12−12$ 1.178 $2323$ 1.179 $−52−52$ 1.180 $3232$ 1.181 six and seven tenths 1.182 five and eight tenths 1.183 negative thirteen and four hundred sixty-one thousandths 1.184 negative two and fifty-three thousandths 1.185 13.068 1.186 5.094 1.187 1.05 1.188 9.17 1.189 6.58 6.6 7 1.190 15.218 15.22 15.2 1.191 16.49 1.192 23.593 1.193 0.42 1.194 12.58 1.195 $−27.4815−27.4815$ 1.196 $−87.6148−87.6148$ 1.197 25.8 258 2,580 1.198 142 1,420 14,200 1.199 587.3 1.200 34.25 1.201$0.19

1.202

259.

32, negative

261.

263.

### Section 1.4 Exercises

265.

$−32−32$

267.

$−63−63$

269.

$−6−6$

271.

14

273.

$−4−4$

275.

13

277.

$−12−12$

279.

$−47−47$

281.

64

283.

$−16−16$

285.

90

287.

9

289.

41

291.

$−9−9$

293.

$−29−29$

295.

5

297.

$−47−47$ 16

299.

$−4−4$ 10

301.

$−8−8$

303.

$−16−16$

305.

121

307.
1. 1
2. 33
309.

$−5−5$ 25

311.

21

313.

$−56−56$

315.

$(3+(−15))+7;−5(3+(−15))+7;−5$

317.

$10−(−18);2810−(−18);28$

319.

$−5−(−30);25−5−(−30);25$

321.

$−3·15;−45−3·15;−45$

323.

$−60÷(−20);3−60÷(−20);3$

325.

$−6a+b−6a+b$

327.

$−10(p−q)−10(p−q)$

329.

$96°96°$

331.

21

333.

$−28−28$

335.

$187 337. $−3600−3600$ 339. Answers may vary 341. Answers may vary ### Section 1.5 Exercises 343. $616,924,1232616,924,1232$ answers may vary 345. $1018,1527,20361018,1527,2036$ answers may vary 347. $−511−511$ 349. $−127−127$ 351. $10211021$ 353. $−x4y−x4y$ 355. $2x23y2x23y$ 357. $27402740$ 359. $1414$ 361. $−16−16$ 363. $−2150−2150$ 365. $11301130$ 367. $20112011$ 369. 9n 371. $−34−34$ 373. $9898$ 375. $4949$ 377. $334x334x$ 379. $−49−49$ 381. $10u9v10u9v$ 383. $−10−10$ 385. $−116−116$ 387. $−109−109$ 389. $−25−25$ 391. $2m3n2m3n$ 393. $5252$ 395. $163163$ 397. 0 399. $1313$ 401. $3535$ 403. $28172817$ 405. $9797$ 407. $−8−8$ 409. $116116$ 411. $5252$ 413. $rs+10rs+10$ 415. $x−y−3x−y−3$ 417. $(2)(34);32(2)(34);32$ cups answers will vary 419. 20 bags 421. Answers may vary 423. Answers may vary ### Section 1.6 Exercises 425. $11131113$ 427. $x+34x+34$ 429. $−58−58$ 431. $717717$ 433. $−1613−1613$ 435. $415415$ 437. $1212$ 439. $5757$ 441. $5y−785y−78$ 443. $−38u−38u$ 445. $1515$ 447. $−29−29$ 449. $−14−14$ 451. $n−45n−45$ 453. $−524−524$ 455. $2929$ 457. $914914$ 459. $4949$ 461. $29242924$ 463. $148148$ 465. $724724$ 467. $3712037120$ 469. $1710517105$ 471. $−5340−5340$ 473. $112112$ 475. $158158$ 477. $4x+3124x+312$ 479. $5y−12205y−1220$ 481. $5656$ 4 483. $25n1625n16$ $25n−163025n−1630$ 485. $5454$ 487. $124124$ 489. $13181318$ 491. $−28−15y60−28−15y60$ 493. $33643364$ 495. 54 497. $49254925$ 499. $154154$ 501. $521521$ 503. $7979$ 505. $−5−5$ 507. $19121912$ 509. $23242324$ 511. $115115$ 513. 1 515. $133133$ 517. $−12−12$ $−1−1$ 519. $1515$ $−1−1$ 521. $1515$ $6565$ 523. $−19−19$ 525. $−511−511$ 527. $7878$ yard 529. Answers may vary ### Section 1.7 Exercises 531. 29.81 533. 0.7 535. 0.029 537. $−11.0009−11.0009$ 539. five and five tenths 541. eight and seventy-one hundredths 543. two thousandths 545. negative seventeen and nine tenths 547. 0.7 549. 2.8 551. 0.85 553. 0.30 555. 4.10 557. 5.78 5.8 6 559. 63.48 63.5 63 561. 24.48 563. $−9.23−9.23$ 565. $−40.91−40.91$ 567. $−7.22−7.22$ 569. $−27.5−27.5$ 571. 15.73 573. 102.412 575. 51.31 577. $−4.89−4.89$ 579. 0.144 581. 42.008 583. $−11.653−11.653$ 585. 337.8914 587. 1.305 589. 92.4 591. 55,200 593. 0.19 595.$2.44

597.

3

599.

$−4.8−4.8$

601.

35

603.

2.08

605.

20

607.

$125125$

609.

$13251325$

611.

$5454$

613.

$3838$

615.

$1920019200$

617.

0.85

619.

2.75

621.

$−12.4−12.4$

623.

$1.36—1.36—$

625.

$0.135—0.135—$

627.

3.025

629.

0.01

631.

0.63

633.

1.5

635.

0.214

637.

0.078

639.

1%

641.

135%

643.

300%

645.

8.75%

647.

225.4%

649.

821.

823.

### Section 1.10 Exercises

825.

72 inches

827.

1.5 feet

829.

$53135313$ yards

831.

7,920 feet

833.

9,200 pounds

835.

$17121712$ tons

837.

5,400 s

839.

$9696$ teaspoons

841.

$224224$ ounces

843.

$114114$ gallons

845.

76 in.

847.

65 days

849.

115 ounces

851.

8 lbs. 13 oz.

853.

3.05 hours

855.

10 ft. 2 in.

857.

4 yards

859.

5,000 meters

861.

155 centimeters

863.

3.072 kilometers

865.

1.5 grams

867.

91,600 milligrams

869.

2,000 grams

871.

0.75 liters

873.

91 centimeters

875.

855 grams

877.

2.1 kilograms

879.

1.6 liters

881.

190.5 centimeters

883.

21.9 meters

885.

750 kilograms

887.

3.1 miles

889.

44 pounds

891.

53.2 liters

893.

$30°C30°C$

895.

$40°C40°C$

897.

$22.2°C22.2°C$

899.

$−17.8°C−17.8°C$

901.

$41°F41°F$

903.

$14°F14°F$

905.

$71.6°F71.6°F$

907.

$109.4°F109.4°F$

909.

14.6 kilograms

911.

### Review Exercises

913.

tens ten thousands hundreds ones thousands

915.

ten millions tens hundred thousands millions ten thousands

917.

six thousand, one hundred four

919.

three million, nine hundred seventy-five thousand, two hundred eighty-four

921.

$315315$

923.

$90,425,01690,425,016$

925.

$410410$ $8,5608,560$

927.

$865,000865,000$ $865,000865,000$ $860,000860,000$

929.

$by2,3,6by2,3,6$

931.

$by3,5by3,5$

933.

$by2,5,10by2,5,10$

935.

$2·2·3·5·72·2·3·5·7$

937.

$3·3·5·53·3·5·5$

939.

$2·2·2·3·5·132·2·2·3·5·13$

941.

$2·2·2·3·32·2·2·3·3$

943.

$2·2·3·3·72·2·3·3·7$

945.

$3030$

947.

120

949.

25 minus 7, the difference of twenty-five and seven

951.

45 divided by 5, the quotient of forty-five and five

953.

forty-two is greater than or equal to twenty-seven

955.

3 is less than or equal to 20 divided by 4, three is less than or equal to the quotient of twenty and four

957.

expression

959.

243

961.

13

963.

10

965.

41

967.

34

969.

81

971.

58

973.

12

975.

$12and3,n2and3n212and3,n2and3n2$

977.

$11x2,3x,611x2,3x,6$

979.

$26a26a$

981.

$12x+812x+8$

983.

$12p+212p+2$

985.

$8+128+12$

987.

$x−4x−4$

989.

$6y6y$

991.

$b+15b+15$

993.

> < < >

995.

8 $−1−1$

997.

19

999.

$−3−3$ 3

1001.

7 25 0

1003.

< =

1005.

4

1007.

80

1009.

28 15

1011.

$−135−135$

1013.

0

1015.

132

1017.

6

1019.

9 9

1021.

17 17

1023.

29

1025.

$−48−48$

1027.

$−42−42$

1029.

18

1031.

$−20−20$

1033.

$−35−35$

1035.

$3636$

1037.

$−4−4$

1039.

6

1041.

43

1043.

$−125−125$

1045.

$−88−88$

1047.

$−5−5$

1049.

55

1051.

$−18−18$ $−87−87$

1053.

$−5−5$ 17

1055.

8

1057.

38

1059.

$(−4+(−17))+32;11(−4+(−17))+32;11$

1061.

$−45−9;5−45−9;5$

1063.

84 degrees

1065.

$28,312,41628,312,416$ answers may vary

1067.

$1012,1518,20241012,1518,2024$ answers may vary

1069.

$1313$

1071.

$3434$

1073.

$−78−78$

1075.

$xyxy$

1077.

$215215$

1079.

$−29−29$

1081.

$7p7p$

1083.

$−42−42$

1085.

2

1087.

$−75−75$

1089.

$254a254a$

1091.

$2929$

1093.

$−125−125$

1095.

$3434$

1097.

$−310−310$

1099.

$3r5s3r5s$

1101.

$158158$

1103.

$−6−6$

1105.

$4343$

1107.

$−4−4$

1109.

$5252$

1111.

$−2−2$

1113.

$cd+9cd+9$

1115.

$5959$

1117.

$y+23y+23$

1119.

$−12−12$

1121.

$3535$

1123.

$y−917y−917$

1125.

$−11d−11d$

1127.

$815815$

1129.

$310310$

1131.

$17121712$

1133.

$13241324$

1135.

$19801980$

1137.

$116116$

1139.

$12751275$

1141.

14

1143.

$3838$ 0

1145.

$5959$

1147.

$−6−6$

1149.

8.03

1151.

0.001

1153.

seven and eight tenths

1155.

five thousandths

1157.

5.79 5.8 6

1159.

12.48 12.5 12

1161.

27.73

1163.

−5.53

1165.

−13.5

1167.

35.8

1169.

42.51

1171.

0.12

1173.

26.7528

1175.

2.2302

1177.

0.03

1179.

\$0.71

1181.

150

1183.

$225225$

1185.

$17401740$

1187.

$7474$

1189.

0.4

1191.

$−0.375−0.375$

1193.

$0.5–0.5–$

1195.

7

1197.

0.05

1199.

0.4

1201.

1.15

1203.

18%

1205.

0.9%

1207.

150%

1209.

8

1211.

−5

1213.

$9191$ $847100847100$

1215.

$0.84,1.3–0.84,1.3–$ $0.79132…,0.79132…,$

1217.

rational irrational

1219.

not a real number real number

1221.

$0,160,16$ $−4,0,16−4,0,16$ $−4,0,56,16−4,0,56,16$ $18,5.2537…18,5.2537…$ $−4,0,56,16,18,5.2537…−4,0,56,16,18,5.2537…$

1223. 1225. 1227.

<

1229.

<

1231. 1233. 1235.

>

1237.

<

1239.

$−48m−48m$

1241.

$a+47a+47$

1243.

37

1245.

$359359$

1247.

$17121712$

1249.

$27x+23y27x+23y$

1251.

$−13−13$ $−5.1−5.1$ 14 $8585$

1253.

$110110$ $−94−94$ $5353$

1255.

0

1257.

undefined

1259.

39

1261.

57

1263.

8

1265.

$7x+637x+63$

1267.

$−18m+3−18m+3$

1269.

$5n−25n−2$

1271.

$−5a−13−5a−13$

1273.

84 inches

1275.

64 inches

1277.

2.7 miles

1279.

105 minutes

1281.

94 ounces

1283.

10 lbs. 6 oz.

1285.

15 feet

1287.

170 centimeters

1289.

0.488 grams

1291.

2,900 grams

1293.

1.12 meter

1295.

0.9 kilograms

1297.

175.3 centimeters

1299.

1.6 miles

1301.

14.6 gallons

1303.

35° C

1305.

–6.7° C

1307.

86° F

1309.

10.4° F

### Practice Test

1311.

205,617

1313.

72

1315.

$−2−2$

1317.

$−7−20;−27−7−20;−27$

1319.

677.13

1321.

185%

1323.

99

1325.

$−44−44$

1327.

3

1329.

$169169$

1331.

$m+107m+107$

1333.

$−10.5−10.5$

1335.

2.2365

1337.

$−10p−10p$

1339.

$15x+4y15x+4y$

1341.

undefined

1343.

100 minutes

1345.

4.508 km

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