LESSON Answers for the lesson “Solve Inequalities 5.1 ...€¦ · Answers for the lesson “Solve Inequalities ... 1, 2, 3, 4, 5, 6, 7, 8, 9, ... if it is equivalent to a false

Skill Practice

1. open, left of 28

2. No; because the solution of x 1 7 18 is x 11, the two inequalities do not have the same solution.

3. s 60

4020 60 80

4. a 16

14 16 18 20 22

5. h > 48

4846 50 52 54

6. x 24 7. x < 10

8. x > 4 9. x 22

10. x < 1

22 21 10 2

11. y 216

210212214216218

12. m 24 1 } 4 1

424

26 25 24 23 22

13. n 2 1 } 5

0 1 2 321

215

14. v > 215.8

217 216 215 214 213

215.8

15. w > 217.6

216 214 212218

217.6

16. r < 21

23 22 21 0 1

17. s 9

15131197

18. p 7

5 7 9 11 13

19. q > 21 1 } 6

0 2 42224

1621

20. c 8.8

0 2 4 6 8 10

8.8

21. d > 26.84

24 222628

26.84

22. 8 must be subtracted from both sides of the equation, not subtracted from one and added to the other; x 1 8 2 8 23 2 8, x < 211.

213 212 211 210 29

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d.Answers for the lesson “Solve Inequalities Using Addition and Subtraction”

125Algebra 1

Answer Transparencies for Checking Homework

LESSON

5.1

23. The number line should be shaded to the right of 23, not the left.

2122232425

24. 11 1 m > 223; m > 234

235 234 233 232 231

25. n 2 15 37; n 52

5352515049

26. c 2 13 < 219; c < 26

212 210 28 26 24

27. x < 21.6 28. x 3.3

29. No; no; there are an infinite number of solutions of an inequality, so it is not possible to check them all. One solution might check in the inequality while another does not. For example, if you incorrectly solve x 1 7 > 10 as x > 2, the solution x 5 4 checks in the original inequality.

30. x < 17.7

18 1916 1715

17.7

Problem Solving

31. more than 8350 points

32. at least 33 goals

33. a. s > 127.53

b. Yes; no; no; 128.13 > 127.53; 126.78 < 127.53; when your score is 127.53, you and your competitor will tie.

34. C

35. Sample answer: You want to improve on your personal best of 16 points scored in a basketball game. In the first three quarters of the game, you scored 14 points. Write and solve an inequality to find the possible number of points that you can score in the fourth quarter to give yourself a new personal best; x 3, if you score at least 3 points in the fourth quarter, you will have a new personal best.

36. 2 axles: w 19,800 lb, 3 axles: w 39,800 lb, 4 axles: w 54,800 lb, 5 axles: w 65,800 lb; no; the total weight, 34,200 pounds, would exceed the maximum weight allowed, 34,000 pounds.

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126Algebra 1


37. a.

OriginalPrice, x($) 19,459 19,989

FinalPrice, y ($) 16,459 16,989

OriginalPrice, x($) 20,549 22,679

FinalPrice, y ($) 17,549 19,679

OriginalPrice, x($) 23,999

FinalPrice, y ($) 20,999

b. x 2 3000 17,000, x 20,000

38. a. at most 53.92 sec

b. Yes; with a fastest time of 53.18 seconds and an average time of 53.92 seconds, his slowest time must be greater than 53.92 seconds. If his time is between 53.92 seconds and his slowest time, the team will not meet its goal.

39. at least $35,682

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127Algebra 1


Skill Practice

1. Division property of inequality

2. No; when you multiply both sides

of x } 24 < 29 by 24 you must

reverse the inequality symbol, producing the inequality x > 36.

3. p 7

1612840

7

4. x > 30

0 20 40 60

5. y > 6

86420

6. w < 200

0 200 4002400 2200

7. q < 28

403020100

28

8. r 8

0 4 8 12 16

9. g > 2120

0 100210022002300

2120

10. m 2

0 2 4 622

11. t 222.5

0220 210230240

222.5

12. n < 227 227

0240 230 220 210

13. s 25

024 222628

14. v 32 32

400 20240 220

15. f < 20.25

0.5020.52121.5

16. d 237.2 237.2

0240 230 220 210

17. c < 20.6

020.4 20.220.620.8

18. k 0.49 0.49

0.5021.5 21 20.5

19. z 20.25

0.5020.52121.5

20. x 37.5

200 40 60 80

37.5

21. j < 20.34

020.4 20.220.620.8

20.34

22. y 45 45

0 20 40 60 80

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d.Answers for the lesson “Solve Inequalities Using Multiplication and Division”

129Algebra 1


LESSON

5.2

23. r > 254

0 20220240260

254

24. p 20.38 20.38

020.8 20.6 20.4 20.2

25. m > 224

0 10210220230

224

26. t < 0.61 0.61

0 0.2 0.4 0.6 0.8

27. In both cases, you divide both sides of the inequality by a; when a > 0, you do not reverse the inequality symbol, but when a < 0, you do.

28. The inequality symbol was not reversed when dividing both sides

by 215; 215x } 215 < 45 }

215 , x < 23.

29. Both sides of the inequality were multiplied by a positive number, so the inequality symbol should not have been reversed; x 263.

30. 8x > 50; x > 25 } 4

0 2 4 6 8

254

31. 215y 90; y 26

022242628

32. v } 29 < 218; v > 162

162

0 50 100 150 200

33. w } 24 2 1 } 6 ; w 24

0 2222426

34. Sample answer: 23x < 212

Problem Solving

35. a. Negative; when you divide both sides of the inequality by the negative number a, the inequality symbol becomes

< and b } a is negative, because

(1)4(2) 5 (2). Thus, the answer is in the form x < (a negative number), so x itself must be negative.

b. Positive; when you divide both sides of the inequality by the positive number a, the inequality symbol stays the

same and b } a is positive,

because (1)4(1) 5 (1). Thus, the answer is in the form x > (a positive number), so x itself must be positive.Co

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Har

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eser

ved.

130Algebra 1


35. c. Both; when you divide both sides of the inequality by the positive number a, the inequality symbol stays the

same and b } a is negative,

because (2)4(1) 5 (2). Thus, the answer is in the form x > (a negative number), so x itself can be either positive or negative (or 0).

d. Both; when you divide both sides of the inequality by the negative number a, the inequality symbol becomes

< and b } a is positive, because

(2)4(2) 5 (1). Thus, the answer is in the form x < (a positive number), so x itself can be either positive or negative (or 0).

36. at most 5 CDs

37. at least 200 words

38. a. at most 16 books

b. 4x 66, x 16.5, at most 16 books

c. y 5 4x;

0 2 4 6 8 10 12 14 16 18 !

"

0102030405060708090

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

d. Answers may vary.

39. at least 3.2

40. d < 18(0.75), d < 13.5, less than 13.5 miles

41. a. 400h 6560, h 16.4; no more than 16 horses

b. No; the area added by increasing both the length and the width by 20 feet can be divided into 2 rectangles (80 feet by 20 feet and 82 feet by 20 feet) and 1 square (20 feet by 20 feet). The 400 square feet of the square is large enough to hold one horse, and the rectangular areas will be able to hold additional horses.

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131Algebra 1


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41. c. no more than 23 horses; the area of the new corral is (80 1 15)(82 1 15) 5 9215 square feet. Find the possible numbers, h, of horses the corral can hold by solving the inequality 9215 400h; h 23.04.

42. decreases of at least $102.63

132Algebra 1


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Skill Practice

1. equivalent inequalities

2. An inequality has no solutions if it is equivalent to a false inequality such as 0 > 2. All real numbers are solutions of the inequality if it is equivalent to a true inequality such as 0 < 2.

3. x > 5

91 3 5 7

4. y 21

26 24 0 222

5. v 21

1 3 52123

6. w < 212

0216 212 28 24

7. r 1 1 } 7

0 1 2 321

171

8. s 4

22 0 2 4 6

9. m > 3

1 3 5 721

10. n < 21 2 } 9 2

921

23 22 21 0 1

11. p < 1 } 2

0 1212223

12. q 58

0 20 40 60 80

58

13. d > 210

22226210214

14. f > 218 1 } 3

0 10230 220 210

13218

15. The inequality symbol was not reversed when dividing both sides by 23; x 213.

16. The distributive property was not used correctly; 28x 1 12 < 28, 28x < 16, x > 22.

17. all real numbers

18. d 0 19. s 0




23. no solution 24. no solution

25. no solution



Answers for the lesson “Solve Multi-Step Inequalities”

134Algebra 1


LESSON

5.3

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29. 3x 1 4 < 40; x < 12

0 4 8 12 16

30. 2(x 1 8) 236; x 226

0240 230 210220

226

31. 5x 1 2x > 9x 2 4; x < 2

0 2 42224

32. 6(6x 2 3) 22(4 1 8x); x 5 } 26

0 0.4 0.820.8 20.4

526

33. C

34. 9(x 1 2) > 81; x > 7

35. 1 } 2 8(x 1 1) 44; x 10

36. 215

Problem Solving

37. at most 11 songs

38. at least 6 ornaments

39. a. Up to 6 swans; the area of the habitat is (20 feet)(50 feet) 5 1000 square feet. 500 square feet are needed for the first two swans and the remaining 1000 2 500 5 500 square feet can hold up to 500 4 125 5 4 more swans; so, the maximum number of swans is 2 1 4 5 6 swans.

b. at most 14 more swans

40. C

41. a.

Pitches perinning, p 15 16 17

Total numberof pitches, t 98 101 104

Pitches perinning, p 18 19

Total numberof pitches, t 107 110

b. 53 1 3p 105, p 17 1 } 3 , at most 17 pitches

42. a. 5%; the amount that was taxed was $300 2 $175 5 $125. To find the tax rate, solve the

proportion x } 100 5 6.25

} 125 .

b. p 1 0.05( p 2 175) 400, p 389.29; up to $389.29

135Algebra 1


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42. c. More than $875; for price p > 175 the tax paid in the 4% sales tax state is 0.04p, and the tax paid in the other state is 0.05( p 2 175), or 0.05p 2 8.75. To find the values of p for which the first expression is less than the second, solve the inequality 0.04p < 0.05p 2 8.75 to get

p > 8.75 } 0.01 , or p > 875. Check

p 5 $900: The tax paid in the 4% sales tax state is 0.04($900) 5 $36 and the tax paid in the other state is 0.05($900) 2 $175) 5 $36.25.

43. at least 196

136Algebra 1


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Skill Practice

1. compound inequality

2. The graph of 26 x 24 consists of 26, 24 and all the points on the number line between 26 and 24. The graph of x 26 or x 24 consists of 26 and all the points on the number line to the left of 26, along with 24 and all the points on the number line to the right of 24.

3. 2 < x < 6

1 3 5 721

4. x 28 or x > 12

160 4 8 12212 28 24

5. 21.5 x < 9.2

0 4 8 1224

21.5 9.2

6. x 210 or x 27 1 } 2

211 210 2829 27 26

1227

7. 40 s 60

20 30 40 50 60

8. t < 60 or t > 75

55 60 7065 75 80

9. 1 < x 6

1 3 5 721

10. 24 y < 1

20 426 24 22

11. 24 m 1 } 4

021222324

14

12. 25 n < 4

20 426 24 22

13. 2 1 } 3 p < 2

0 1 2

213

14. 25 1 } 4 q < 21 1 } 4 1

425 1421

28 026 24 22

15. r < 2 or r 7

420 6 8

16. s < 222 or s 3 222 3

0 10230 220 210

17. v < 25 or v > 5

0 4 82428

25 5

18. w < 217 or w > 5 217

0 10230 220 210

19. g < 22 1 } 3 or g > 10

0 4 8 1224

1322

Answers for the lesson “Solve Compound Inequalities”

138Algebra 1


LESSON

5.4

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20. h < 24 or h 28 24 28

0 10 20 30 40210

21. 3 was subtracted from only two of the three expressions of the inequality; 1 < 22x < 6,

2 1 } 2 > x > 23.

0212223

22. The graph should include the points of the number line to the left on 210 and to the right of 7, not the points between 210 and 7.

7

0 5 10215 210 25

210

23. x 1 5 < 8 or x 2 3 > 5; x < 3 or x > 8

1 3 5 7 9

24. 24 < x 2 3 < 21; 21 < x < 2

1 2 322 21 0

25. 28 3(x 2 4) 10; 1 1 } 3 x 7 1 } 3

2 4 6 80

131 1

37

26. 22x 1 8 25 or 6 < 22x;

x < 23 or x 6 1 } 2

23

0 4 828 24

126

27. C

28. False. Sample answer: a 5 25

29. true

30. True; any solution of x < 5 and x 24 lies between 24 and 5 on the number line, so it is to the left of 5 and is therefore a solution of x < 5.

31. False. Sample answer: a 5 23 is a solution of x > 5 or x 24, but it is not a solution of x > 5.

32. a. x 1 5 > 7, x > 2; 5 1 7 > x, x < 12; x 1 7 > 5, x > 22

b. 2 < x < 12

c. Sample answer: 3, 7, 10

33. no solution

22 21 0 1 2

34. y > 7

1 3 5 7 9

35. m > 25

0 226 24 22


0 2 424 22

Problem Solving

37. 22600 e 2100;

0 1000210002200023000

210022600

139Algebra 1


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38. 24 t 5

0 2 4 62426 22

5

39. C

40. 5319 p 73,486

41. 3.2 lb f 6.4 lb

42. less than 129.31 cm or greater than 189.66 cm

43. a. 5 } 9 (F 2 32) < 0 or

5 } 9 (F 2 32) > 100, F < 328F

or F > 2128F

b. 238F, 2398F;

8F 23 86 140 194 239

8C 25 30 60 90 115

44. from 108F to 158F

45. a. 8 w } 300

10,

2400 w 3000; 2400 watts to 3000 watts

b. Yes; no; the amplification per person for 350 people is

2900 } 350 ø 8.3 watts, which is

between 8 watts and 10 watts, the amplification for 400

people is 2900 } 400 5 7.25 watts,

which is not between 8 watts and 10 watts.

c. 4800 watts; because each person requires at least 8 watts of amplification, and you want to be sure to provide enough amplification for 600 people, you need at least 8(600) 5 4800 watts of amplification.

46. from $34.78 up to $69.57

Mixed Review of Problem Solving

1. a. from 1228F to 9328F

b. 932122

200 400 600 800 10000

c. No; the thermometer cannot measure temperatures higher than 9328F.

2. a. x 78

b. No; with a score of 100 your average will be

402 1 100 } 6 5

502 } 6 ø 84.

140Algebra 1


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3. 3 cartons; 3

4. a. up to $130

b. 4.75s 130; up to 27 pairs of socks

5. Sample answer: The solution x 14.12 means that the greatest number that will make the inequality true is 14.12.

6. a. at most 213 1 } 3 lb

b. Yes; since the most the adults weigh is 200 pounds, and that is less than what the average weight needs to be, all the people and baggage can be accommodated on the raft.

7. a. 18 t 300

b. Greater than $10,000; their taxes are higher than $300, the highest tax paid by people with annual incomes of $10,000 or less; from $12,000 up to $19,000.

c. Greater than $20,000; the inequality to describe the situation is 0.04x < 0.03(10,000) 1 0.05 (x 2 10,000). Solving the inequality gives x > $20,000.

141Algebra 1


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Skill Practice

1. absolute value equation

2. The absolute deviation of x from 9 is 5.

3. 5, 25 4. 36, 236

5. 0.7, 20.7 6. 9.2, 29.2

7. 1 } 2 , 2 1 } 2 8. 7 } 4 , 2 7 } 4

9. 4, 210 10. 5 3 } 4 , 23 1 } 4

11. 21, 23 2 } 3 12. 27, 211

13. 2, 29 14. 22, 26

15. 4, 9 16. 7, 25

17. 8 1 } 2 , 23 1 } 2 18. 1, 24 1 } 3

19. 2 1 } 2 , 22 1 } 2 20. 0, 2 2 } 5

21. The absolute value symbol was removed without writing the second equation, x 1 4 5 213; x 5 9 or x 5 217.

22. The absolute value of a number is never negative, so it is incorrect to rewrite this absolute value equation as two equations; there are no solutions.


25. 24.5, 25.5 26. no solution

27. 23, 6 28. 25, 210

29. 13 1 } 2 , 14 1 } 2 30. no solution

31. 1 } 4 , 21 1 } 4 32. D

33. 13, 23 34. 25, 15

35. 27.5, 210.7 36. 3.3, 210.1

37. The distance between x and 3 is 7, 10, 24; x 2 3 5 7 or x 2 3 5 27, 10, 24; the solutions are the same.

38. x 2 3 1 4 5 8; 7, 21

39. 5 2x 1 9 5 15; 23, 26

40. Yes; no; yes; when a 5 3 and x 5 22, 3 22 5 3(2) 5 6 5

26 5 3(22) ; when a 5 23 and x 5 22, 23 22 5 23(2) 5 26 ! 6 5 23(22) ; when a 5 0 and x 5 22, 0 22

5 0 5 0 5 0(22) .

41. one, two

Problem Solving

42. 39 in., 45 in.

43. 235 sec, 245 sec

44. C

45. a. 52.462 points, 56.888 points

b. 0.3 point

46. 11.4 carats, 12.6 carats

Answers for the lesson “Solve Absolute Value Equations”

143Algebra 1


LESSON

5.5

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47. a. p 5 s 2 450

b. 300 points, 600 points

48. a. 1920 b. 2019

c. No; if you substitute 4 for p in the model, the equation has no solution.

49. a. June 2005; November 2005

b. Yes; make a table of values for (m, p) using integer values of m from 0 to 8. Look for the lowest value of p in the table.

50. t 2 115.76 1.72

144Algebra 1


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Skill Practice

1. equivalent inequalities

2. Solving x 5 involves solving a compound inequality with and, while solving x 5 involves solving a compound inequality with or.

3. 24 < x < 4

0 2 42224

4. y 23 or y 3

0 2 424 22

5. h < 24.5 or h > 4.5

0 4 82428

4.524.5

6. 21.3 < p < 1.3

22 21 0 1 2

21.3 1.3

7. 2 3 } 5 t 3 }

5

0 121

8. j 21 3 } 4 or j 1 3 } 4

22 21 0 1 2

3413

421

9. d 27 or d 21

0 42428212

27 21

10. 25 < b < 15

210 25 10 150 5 20

11. m < 220 or m > 8

4 12 20 2824

12. 3 < s < 4

3 41 20

13. c 23 or c 1 } 2

1 325 23 21

2312

14. 1 n 3.5

3 41 20

3.5

15. r < 28 or r > 24

2214 210 26 22

16. s < 23 or s > 13 1 } 2 1

213

26 12 180 6

17. u 23 1 } 5 or u 6 2 } 5

0 2 4 6 828 26 24 22

1523 2

56

18. 24 < w < 21 1 } 3 1

321

24 23 22 21 0

19. v < 6 or v > 34

6 18 30 4226

34

20. f 212 or f 9

0 6 12218 212 26

9

Answers for the lesson “Solve Absolute Value Inequalities”

146Algebra 1


LESSON

5.6

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21. B

22. When the inequality has the absolute value expression isolated on the left side, the equivalent compound inequality will use and if the symbol is < or , and it will use or if the symbol is > or .

23. The compound inequality should use or: x 1 4 > 13 or x 1 4 < 213; x > 9 or x < 217.

24. Part of the compound inequality is missing; the compound inequality should be 220 < x 2 5 < 20; 215 < x < 25.

25. x 2 6 4; 2 x 10

2 6 10 1422

26. 2x 1 7 15; x 211 or x 4

0 4 8212216 28 24

211

27. 24x 2 7 1 3 > 10; x < 23.5 or x > 0

0 2222426

23.5

28. 4 x 2 9 < 8; 7 < x < 11

5 7 9 11 13

29. true

30. False. Sample answer: 220

31. False. Sample anwser: 20

32. true

33. 6 < x < 7; solve each absolute value inequality by rewriting it as a compound inequality. Graph the solutions and find the intersection of the graphs.

34. No solution; all real numbers; because an absolute value cannot be negative, ax 1 b is never less than any negative number c, and is always greater than any negative number c.

Problem Solving

35. at least 470 words and at most 530 words

36. greater than 0.5 or less than 20.5

37. t 2 346 2, at least 3448F and at most 3488F; continue to preheat; the temperature is still below 3508F.

38. a.

Measuredcompression,p (lb)

275 325 375

Absolutedeviationfrom 350 (lb)

75 25 25

Measuredcompression, p (lb) 425 475

Absolutedeviation from350 (lb)

75 125

147Algebra 1


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38. b. p 2 350 50, at least 300 lb and at most 400 lb; 325, 375

39. a. 10.02 m/sec2

b. 0.88 m/sec2

40. a. 3600 antelope

b. p 2 18,000 3600; at least 14,400 antelope and at most 21,600 antelope.

c. No; if the relative absolute deviation is 25%, then the actual population is between 13,500 and 22,500 antelope. For the 25% relative absolute deviation the actual population might be 14,000 antelope, which is less than any possible actual population for the 20% relative absolute deviation.

41. at least 3 minutes 10 seconds and less than 3 minutes 20 seconds, more than 3 minutes 40 seconds and at most 3 minutes and 50 seconds

148Algebra 1


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Skill Practice

1. solution

2. Graphing a linear inequality in two variables involves graphing the boundary line (as either a solid or dashed line) and then shading the appropriate half-plane. Graphing a linear equation in two variables involves only the graphing of one (solid) line.

3. not a solution 4. solution



9. solution 10. not a solution

11. not a solution

12. solution

13. solution 14. solution

15. C 16. A

17.

!!

"

2!

y > x 1 3

18.

!!

"

2!

y ! x 2 2

19.

!!

"

2!

y < 3x 1 5

20.

"!

"

2"

y " 22x 1 8

Answers for the lesson “Graph Linear Inequalities in Two Variables”

150Algebra 1


LESSON

5.7

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21.

"!

"

2"

x 1 y < 28

22.

"

!

"

2"

x 2 y ! 211

23.

#!

"

x 1 8y > 16

"

24.

!!

"

2!

5x 2 y " 1

25.

!!

"

2!

2(x 1 2) > 7y

26.

!!

"

2!

y 2 4 < x 2 6

151Algebra 1


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27.

$

!

"

2!

24y ! 16x

28.

!!

"

2!

6(2x) " 224y

29.

!

!

"

2!

y < 23

30.

!!

"

2!

x " 5

31.

!!

"

2!

x > 22

32.

!!

"

2!

y ! 4

152Algebra 1


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33. "!

"

"

3(x 2) > y 8

34.

!!

"

!

x 4 ! 2(y 6)

35.

#!

"

(x 2) 3y < 812

"

36.

!

"

2(x 1) " y 114

"

!"

37. The wrong half-plane is shaded.

"

!

"

2!

2y 2 x $ 2

38. The boundary line should be solid.

!!

"

2!

x ! 23

39. No; (0, 0) is a point on the boundary line 2x 5 25y.

153Algebra 1


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40. x 2 4 y

!!

"

2!

x 2 4 " y

41. 22y x 1 6

!!

"

2!

22y ! x 1 6

42. y } 2 > 7 2 x

"

!

"

2"

> 7 2 xy2

43. x 1 4y < 23

!!

"

x 4y < 3

$

44. y > 2 5 } 4 x 1

7 } 4

45. y 5 } 7 x 2

9 } 7

46. y > 1 } 2 x 1 2

47. y > 0

48. x < 0

49. y < 0

50. x > 0

51. y 2x 1 1

"

!

"

y ! 2x 1

"

154Algebra 1


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52. y < 3x 1 5

!!

"

y < 3x 5

!

Problem Solving

53.

Weight of bobsled (pounds)

Wei

ght

of a

thle

tes

(pou

nds)

0 200 400 600 800 !

"

0100200300400500600700800900

x 1 y ! 860

Sample answer: The solution (450, 400) means that the bobsled can weigh 450 pounds when the combined weight of the athletes is 400 pounds.

54.

Maximum weight (pounds)

Num

ber

of p

asse

nger

s

0 200 400 600 800 !

"

0123456789

y ! x150

Sample answer: The solution (1200, 8) means that the elevator can have 8 passengers when the elevator’s maximum weight capacity is 1200 pounds.

55. a. 15x 1 10y 100

b.

Spanish (hours)

Fren

ch (h

ours

)

0 1 2 3 4 5 6 7 8 9 !

"

0123456789

1011

15x 1 10y " 100

(4, 8), (5, 3), (6, 1)

155Algebra 1


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55. c. Sample answer:

Spanish time(hours) 4 5 6

French time(hours) 8 3 1

Total earnings(dollars) 140 105 100

56. B

57. a. 1 } 6 m 1 1 } 2 12

Number of muffins

Num

ber

of lo

aves

of b

read

10 30 50 70 900 20 40 60 80 #

l

0

15

25

35

510

20

30

m 16 l ! 121

2

b. m 60

58. a. y 0.3x

Total calories

Fat

calo

ries

0 500 1000 1500 2000 !

"

0100200300400500600700

y ! 0.3x

b. y 500

59. a. x 1 y 30

Duffel weight (pounds)

Bed

roll

wei

ght

(pou

nds)

5 15 25 350 10 20 30 !

"

5

15

25

35

0

10

20

30

x y ! 30

Sample answer: (20, 4), (25, 5), (26, 2)

b. Yes; no; (0, 30) means that you do not take a duffel and have a 30 pound bedroll, while (30, 0) means you take a 30 pound duffel and do not take a bedroll. You need to bring both a duffel and a bedroll.

60. a. y > 110 2 x

Age (years)

Perc

ent

inve

sted

in s

tock

s

0 40 80 120 !

"

020406080

100120140

y > 110 x

156Algebra 1


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60. b. Greater than 80% and up to 100%; substitute x 5 30 into the inequality to get y > 110 2 30, so the investor should invest more than 80% of his money in stocks. The investor cannot invest more than 100% of his money in stocks.

c. Less than or equal to 10 years; when x is less than 10 years, y will be greater than 100%. You cannot invest more than 100% of your money.

61. a. sinks:

Volume (cm3)

Mas

s (g

ram

s)

0 500 1000 1500 $

#

0

500750

250

1000125015001750

m > V

floats:

Volume (cm3)

Mas

s (g

ram

s)

0 500 1000 1500 $

#

0250500750

1000125015001750

m < V

b. Sink; the volume of the cylindrical can is

r2h 5 (25)(10) ø 785.40 cubic centimeters. Since the mass, 2119.5 grams, is greater than the volume, 785.40 cubic centimeters, the can will sink.

Mixed Review of Problem Solving

1. a. 7p 1 5s 36

b.

Number of pies

Num

ber

of p

ints

of a

pple

sauc

e

0 2 31 4 5 6 7 %

&

012345

76

89

7p 1 5s ! 36

157Algebra 1


c. Sample answer: 1 pie and 5 pints of applesauce, 3 pies and 3 pints of applesauce, 4 pies and 1 pint of applesauce

2. a. x 2 4 0.5

b. Yes; the solution of the inequality from part (a) is 3.5 x For at least 80% of your scoops to meet the weight requirement, at least 8 scoops must weigh at least 3.5 ounces and at most 4.5 ounces. Because 8 out of 10 of your scoops are in the required range of weights, you can start working at the shop.

3. 16.5 min; 5 . 6 1

4. Sample answer: During a portion of time spent driving on the highway, your average speed is 50 miles per hour with an absolute deviation of your actual speed from your average speed of 10 miles per hour. What are your minimum and maximum speeds during this time? 40, 60; your minimum speed was 40 miles per hour and your maximum speed was 60 miles per hour.

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158Algebra 1


5. a. a 1 w < 120

Air temperature (8F)

Wat

er t

empe

ratu

re (8

F)

0 40 80 120 '

(

020406080

100120140

a w < 120

b. a < 808F

c. Move the line so that its x- and y-intercepts are 100 instead of 120. The linear inequality that describes the situations in which a protective suit is required is a 1 w < 100.

6. a. $220.25

b. x 2 220.25 50; from $170.25 up to $270.25

c. 6 phones

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159Algebra 1


Documents

LESSON Answers for the lesson “Solve Inequalities 5.1 ...€¦ · Answers for the lesson “Solve Inequalities ... 1, 2, 3, 4, 5, 6, 7, 8, 9, ... if it is equivalent to a false