Intermediate Algebra 2e

# Chapter 1

## Try It

1.1

yes yes no yes
no

1.2

no yes yes no
no

1.3

$2 · 2 · 2 · 2 · 5 2 · 2 · 2 · 2 · 5$

1.4

$2 · 2 · 3 · 5 2 · 2 · 3 · 5$

1.5

$36 36$

1.6

$72 72$

1.7

16

1.8

23

1.9

86

1.10

1

1.11

9 64 40

1.12

216 64 185

1.13

$10 x 2 + 16 x + 17 10 x 2 + 16 x + 17$

1.14

$12 y 2 + 9 y + 7 12 y 2 + 9 y + 7$

1.15

$14x2−1314x2−13$ $12x÷212x÷2$
$z+13z+13$ $8x−188x−18$

1.16

$17y2+1917y2+19$ $7y7y$
$x+11x+11$ $11a−1411a−14$

1.17

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

1.18

$2x−82x−8$ $2(x−8)2(x−8)$

1.19

$w − 7 w − 7$

1.20

$l − 6 l − 6$

1.21

$4 q − 8 4 q − 8$

1.22

$7 n + 3 7 n + 3$

1.23

$==$ $>>$ $<<$
$==$

1.24

$>>$ $==$ $>>$
$<<$

1.25

16

1.26

9

1.27

$−6−6$ 2 $−2−2$

1.28

$−7−7$ 3 $−3−3$

1.29

2 $−2−2$ $−10−10$ 10

1.30

3 $−3−3$ $−11−11$ 11

1.31

$8,88,8$ $−18,−18,$ $−18−18$
$19,1919,19$ $−4,−4,$ $−4−4$

1.32

$8,88,8$ $−22,−22,$ $−22−22$
$23,2323,23$ $3,33,3$

1.33

3

1.34

13

1.35

23 60 $−63−63$ $−9−9$

1.36

39 39 −28 −7

1.37

81 $−81−81$

1.38

49 $−49−49$

1.39

4 21

1.40

9 6

1.41

31

1.42

67

1.43

$( 9 + ( −16 ) ) + 4 ; − 3 ( 9 + ( −16 ) ) + 4 ; − 3$

1.44

$( −8 + ( −12 ) ) + 7 ; − 13 ( −8 + ( −12 ) ) + 7 ; − 13$

1.45

The difference in temperatures was 45 degrees.

1.46

The difference in temperatures was 9 degrees.

1.47

$− 23 40 − 23 40$

1.48

$− 5 8 − 5 8$

1.49

$−33 a −33 a$

1.50

$−26 b −26 b$

1.51

$4 15 4 15$

1.52

$2 3 2 3$

1.53

$3 4 b 3 4 b$

1.54

$4 q 4 q$

1.55

$79 60 79 60$

1.56

$103 60 103 60$

1.57

$27a−323627a−3236$ $2a32a3$

1.58

$24k−53024k−530$ $2k152k15$

1.59

4

1.60

2

1.61

$1 90 1 90$

1.62

272

1.63

2

1.64

$2 7 2 7$

1.65

$− 1 2 − 1 2$

1.66

$2 3 2 3$

1.67

$6.586.58$ $6.66.6$ 7

1.68

$15.21815.218$ $15.2215.22$
$15.215.2$

1.69

$−16.49−16.49$ $−0.42−0.42$

1.70

$−23.593−23.593$ $−12.58−12.58$

1.71

$−27.4815 −27.4815$

1.72

$−87.6148 −87.6148$

1.73

25.8 258 2,580

1.74

142 1,420 14,200

1.75

$587.3 587.3$

1.76

$34.25 34.25$

1.77

$117500117500$ $−0.875−0.875$

1.78

$31253125$ $−0.375−0.375$

1.79

0.09, 0.87, 0.039 17%, 175%, 8.25%

1.80

0.03, 0.91, 0.083 41%, 225%, 9.25%

1.81

6 13 $−15−15$

1.82

4 14 $−10−10$

1.83

$4,494,49$ $−3,4,49−3,4,49$
$−3,0.3–,95,4,49−3,0.3–,95,4,49$ $−2−2$
$−3,−2,0.3–,95,4,49−3,−2,0.3–,95,4,49$

1.84

$6,1216,121$
$−25,−1,6,121−25,−1,6,121$
$−25,−38,−1,6,121−25,−38,−1,6,121$
$2.041975...2.041975...$
$−25,−38,−1,6,121,2.041975...−25,−38,−1,6,121,2.041975...$

1.87

1.88

1.89

$32 r + 29 s 32 r + 29 s$

1.90

$41 m + 6 n 41 m + 6 n$

1.91

$1 7 15 1 7 15$

1.92

$1 2 9 1 2 9$

1.93

$−48 a −48 a$

1.94

$−92 x −92 x$

1.95

$5 49 5 49$

1.96

$11 25 11 25$

1.97

0 undefined

1.98

0 undefined

1.99

$4 x + 8 4 x + 8$

1.100

$6 x + 42 6 x + 42$

1.101

$5 y + 3 5 y + 3$

1.102

$4 n + 9 4 n + 9$

1.103

$70 + 15 p 70 + 15 p$

1.104

$4 + 35 d 4 + 35 d$

1.105

$−10 + 15 a −10 + 15 a$

1.106

$−56 + 105 y −56 + 105 y$

1.107

$− z + 11 − z + 11$

1.108

$− x + 4 − x + 4$

1.109

$3 − 3 x 3 − 3 x$

1.110

$2 x − 20 2 x − 20$

1.111

$5 x − 66 5 x − 66$

1.112

$7 x − 13 7 x − 13$

## Section 1.1 Exercises

1.

Divisible by 2, 3, 6

3.

Divisible by 2

5.

Divisible by 3, 5

7.

$2 · 43 2 · 43$

9.

$5 · 7 · 13 5 · 7 · 13$

11.

$2 · 2 · 2 · 2 · 3 · 3 · 3 2 · 2 · 2 · 2 · 3 · 3 · 3$

13.

24

15.

280

17.

440

19.

5

21.

58

23.

29

25.

149

27.

50

29.

5

31.

64 16 7

33.

21

35.

9

37.

$10 x + 6 10 x + 6$

39.

$22 a + 1 22 a + 1$

41.

$17 x 2 + 20 x + 16 17 x 2 + 20 x + 16$

43.

$5x2−6xy5x2−6xy$ $6y25x6y25x$
$y2+21y2+21$ $81x2−6x81x2−6x$

45.

$4ab2+3a2b4ab2+3a2b$ $20xy220xy2$
$m+15m+15$ $121x2−9x121x2−9x$

47.

$8(y−9)8(y−9)$ $8y−98y−9$

49.

$5(3x+y)5(3x+y)$ $15x+y15x+y$

51.

$2 c + 14 2 c + 14$

53.

$3 n − 7 3 n − 7$

55.

57.

## Section 1.2 Exercises

59.

$>>$ $>>$ $>>$ $>>$

61.

$==$ $==$ $>>$ $==$

63.

0

65.

8

67.

15

69.

1

71.

$−11−11$ $−3−3$ $33$

73.

32

75.

$−22 −22$

77.

$29 29$

79.

6 $−6−6$ $−20−20$ $2020$

81.

$−59 −59$

83.

22

85.

16 16

87.

45 45

89.

0

91.

4

93.

6

95.

$−32−32$ $−65−65$ $−4−4$
$1313$

97.

$−4−4$ $−12−12$ $−39−39$
$1414$

99.

$6464$ $−64−64$

101.

$−47 −47$

103.

$90 90$

105.

$9 9$

107.

$41 41$

109.

$−9 −9$

111.

$−29 −29$

113.

$1 1$

115.

$−3 −3$

117.

$5 5$

119.

$−47−47$ $1616$

121.

$121 121$

123.

$−56 −56$

125.

$6 6$

127.

$( 3 + ( −15 ) ) + 7 ; − 5 ( 3 + ( −15 ) ) + 7 ; − 5$

129.

$10−(−18);2810−(−18);28$
$−25−11;−36−25−11;−36$

131.

$−6 a + b −6 a + b$

133.

$96 ° 96 °$

135.

21 yards

137.

$− 28 − 28$

139.

141.

## Section 1.3 Exercises

143.

$− 12 7 − 12 7$

145.

$10 21 10 21$

147.

$2 x 2 3 y 2 x 2 3 y$

149.

$− 21 a 2 11 b 2 − 21 a 2 11 b 2$

151.

$1 3 1 3$

153.

$− 21 50 − 21 50$

155.

$11 30 11 30$

157.

$9 n 9 n$

159.

$33 4 x 33 4 x$

161.

$− 4 9 − 4 9$

163.

$10 u 9 v 10 u 9 v$

165.

$− 1 16 − 1 16$

167.

$− 10 9 − 10 9$

169.

$− 2 5 − 2 5$

171.

$2 m 3 n 2 m 3 n$

173.

$29 24 29 24$

175.

$1 48 1 48$

177.

$17 105 17 105$

179.

$− 53 40 − 53 40$

181.

$1 12 1 12$

183.

$4 x + 3 12 4 x + 3 12$

185.

$5656$ $44$

187.

$25n1625n16$ $25n−163025n−1630$

189.

$−8x−1518−8x−1518$ $−10k27−10k27$

191.

$−5(a+1)3−5(a+1)3$ $aa$

193.

$9 7 9 7$

195.

$−8 −8$

197.

$11 6 11 6$

199.

$5 2 5 2$

201.

$54 54$

203.

$49 25 49 25$

205.

$15 4 15 4$

207.

$5 21 5 21$

209.

$5 4 5 4$

211.

$1 24 1 24$

213.

$−28 − 15 y 60 −28 − 15 y 60$

215.

$33 64 33 64$

217.

$7 9 7 9$

219.

$−5 −5$

221.

$23 24 23 24$

223.

$11 5 11 5$

225.

$1 1$

227.

$13 3 13 3$

229.

$1515$ $6565$

231.

$− 1 9 − 1 9$

233.

$− 5 11 − 5 11$

235.

237.

## Section 1.4 Exercises

239.

5.78 5.8 6

241.

0.30 0.3 0

243.

63.48 63.5 63

245.

$−40.91 −40.91$

247.

$−7.22 −7.22$

249.

$−27.5 −27.5$

251.

$102.212 102.212$

253.

$51.31 51.31$

255.

$−4.89 −4.89$

257.

$−1200.47982 −1200.47982$

259.

$337.8914 337.8914$

261.

$1.305 1.305$

263.

$92.4 92.4$

265.

2.5

267.

55200

269.

$2.44 2.44$

271.

$−4.8 −4.8$

273.

$2.08 2.08$

275.

$1 25 1 25$

277.

$19 200 19 200$

279.

$0.85 0.85$

281.

$−12.4 −12.4$

283.

$0.71 0.71$

285.

$0.393 0.393$

287.

$156 % 156 %$

289.

$6.25 % 6.25 %$

291.

8

293.

12

295.

$−10 −10$

297.

$0,36,90,36,9$ $−8,0,36,9−8,0,36,9$ $−8,0,125,36,9−8,0,125,36,9$ $1.95286...,1.95286...,$ $−8,0,1.95286...,125,36,9−8,0,1.95286...,125,36,9$

299.

none $−100,−7,−1−100,−7,−1$
$−100,−7,−83,−1,0.77,314−100,−7,−83,−1,0.77,314$
none
$−100,−7,−83,−1,0.77,314−100,−7,−83,−1,0.77,314$

301.
303.
305.
307.
309.

311.

## Section 1.5 Exercises

313.

$27 m + ( −21 n ) 27 m + ( −21 n )$

315.

$5 4 g + 1 2 h 5 4 g + 1 2 h$

317.

$2.43 p + 8.26 q 2.43 p + 8.26 q$

319.

$−63 −63$

321.

$1 5 6 1 5 6$

323.

$17 17$

325.

$14.88 14.88$

327.

$10 p 10 p$

329.

$44 44$

331.

$7 8 7 8$

333.

$d d$

335.

$49 11 49 11$

337.

0

339.

undefined

341.

undefined

343.

$32 y + 72 32 y + 72$

345.

$6 c − 78 6 c − 78$

347.

$3 4 q + 3 3 4 q + 3$

349.

$5 y − 3 5 y − 3$

351.

$3 + 8 r 3 + 8 r$

353.

$36 d + 90 36 d + 90$

355.

$r s − 18 r r s − 18 r$

357.

$y p + 4 p y p + 4 p$

359.

$−28 p − 7 −28 p − 7$

361.

$−3 x + 18 −3 x + 18$

363.

$−3 x + 7 −3 x + 7$

365.

$−3 y − 8 −3 y − 8$

367.

$−33 c + 26 −33 c + 26$

369.

$− a + 19 − a + 19$

371.

$4 m − 10 4 m − 10$

373.

$72 x − 25 72 x − 25$

375.

$22 n + 9 22 n + 9$

377.

$6 c + 34 6 c + 34$

379.

$12 y + 63 12 y + 63$

381.

383.

## Review Exercises

385.

Divisible by $2,3,5,6,102,3,5,6,10$

387.

120

389.

4

391.

3

393.

$6 x 2 − x + 5 6 x 2 − x + 5$

395.

$11(y−2)11(y−2)$ $11y−211y−2$

397.

$==$ $==$ $>>$ $==$

399.

$−9 −9$

401.

8 $−8−8$ $−22−22$ 22

403.

40 40

405.

$−3−3$ $−15−15$ $−56−56$ 17

407.

28

409.

$−12 −12$

411.

9

413.

$( −4 + ( −9 ) ) + 23 ; 10 ( −4 + ( −9 ) ) + 23 ; 10$

415.

$46 ° 46 °$

417.

$− 15 x 3 11 y 2 − 15 x 3 11 y 2$

419.

$8 x 15 y 8 x 15 y$

421.

$31 36 31 36$

423.

$118118$ $5656$

425.

$− 1 6 − 1 6$

427.

75

429.

$− 1 5 − 1 5$

431.

$6.17 6.17$

433.

$96.978 96.978$

435.

488.1813

437.

$56.3 56.3$

439.

$−2.3 −2.3$

441.

$− 48 5 − 48 5$

443.

$1. 27 ¯ 1. 27 ¯$

445.

$4.75 % 4.75 %$

447.

no real number

449.
451.

$3 4 x + y 3 4 x + y$

453.

$1 11 15 1 11 15$

455.

$9 17 9 17$

457.

undefined

459.

$8 b + 10 8 b + 10$

461.

$x p − 5 p x p − 5 p$

463.

$−6 x − 6 −6 x − 6$

465.

$6 y + 16 6 y + 16$

## Practice Test

467.

$7 n + 7 7 n + 7$

469.

$−8 − 11 ; − 19 −8 − 11 ; − 19$

$( −8 − ( −3 ) ) + 5 ; 0 ( −8 − ( −3 ) ) + 5 ; 0$

471.

$28.1528.15$ $28.14628.146$

473.
475.

1

477.

$−8 −8$

479.

$15 17 15 17$

481.

$− 5 3 − 5 3$

483.

$3 3$

485.

$− 7 6 − 7 6$

487.

$−65.4 −65.4$

489.

−160

491.

$1 8 13 1 8 13$

493.

0 undefined

495.

$13 y − 3 13 y − 3$