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Copyright © by Holt, Rinehart and Winston. 45 Algebra 1 All rights reserved. 3-1 Graphing and Writing Inequalities Write the inequality shown by each graph. 1. 2. 3. Graph each inequality. 4. r 1 5. g 2 2 3-2 Solving Inequalities by Adding and Subtracting Solve each inequality and graph the solutions. 6. 4 t 3 7. r 7 12 8. Danny must have at least 410 points to receive an A. He has 275 points. Write and solve an inequality to show the least number of points Danny needs to receive an A. –4 –2 2 4 0 –4 –2 2 4 0 –4 –2 2 4 0 Chapter Review 3 CHAPTER

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  • Copyright by Holt, Rinehart and Winston. 45 Algebra 1All rights reserved.

    3-1 Graphing and Writing Inequalities

    Write the inequality shown by each graph.

    1.

    2.

    3.

    Graph each inequality.

    4. r 1

    5. g 22

    3-2 Solving Inequalities by Adding and Subtracting

    Solve each inequality and graph the solutions.

    6. 4 t 3

    7. r 7 12

    8. Danny must have at least 410 points to receive an A. He has 275 points.Write and solve an inequality to show the least number of points Dannyneeds to receive an A.

    4 2 2 40

    4 2 2 40

    4 2 2 40

    Chapter Review3

    CHAPTER

  • Copyright by Holt, Rinehart and Winston. 45 Algebra 1All rights reserved.

    3-1 Graphing and Writing Inequalities

    Write the inequality shown by each graph.

    1.

    2.

    3.

    Graph each inequality.

    4. r 1

    5. g 22

    3-2 Solving Inequalities by Adding and Subtracting

    Solve each inequality and graph the solutions.

    6. 4 t 3

    7. r 7 12

    8. Danny must have at least 410 points to receive an A. He has 275 points.Write and solve an inequality to show the least number of points Dannyneeds to receive an A.

    p 275 410; p 135; Danny needs at least 135 points to get an A.

    4 28 6 2 4 6 80

    4 28 6 2 4 6 80

    4 2 2 40

    4 2 2 40

    k 04 2 2 40

    y 24 2 2 40

    t 54 2 2 40

    t 7;

    r 5;

    Chapter Review3

    CHAPTER

  • Copyright by Holt, Rinehart and Winston. 46 Algebra 1All rights reserved.

    3-3 Solving Inequalities by Multiplying and Dividing

    Solve each inequality and graph the solutions.

    9. 3k

    2

    10. 3 h2

    11. 2r 6

    12. Hannah wants to buy 4 presents for at least $60. She wants to spend anequal amount of money on each present. Write and solve an inequality toshow the least amount of money Hannah will spend on each present.

    3-4 Solving Two-Step and Multi-Step Inequalities

    Solve each inequality.

    13. c 3c 2 14 14. 23 12 2r 12r

    15. 14 6 22f

    16. 13b 12

    56

    Solve each inequality and graph the solutions.

    17. 5a 2 22

    18. 13 2t 3(t 3)

    CHAPTER 3 REVIEW CONTINUED

  • Copyright by Holt, Rinehart and Winston. 46 Algebra 1All rights reserved.

    3-3 Solving Inequalities by Multiplying and Dividing

    Solve each inequality and graph the solutions.

    9. 3k

    2

    10. 3 h2

    11. 2r 6

    12. Hannah wants to buy 4 presents for at least $60. She wants to spend anequal amount of money on each present. Write and solve an inequality toshow the least amount of money Hannah will spend on each present.

    3-4 Solving Two-Step and Multi-Step Inequalities

    Solve each inequality.

    13. c 3c 2 14 14. 23 12 2r 12r

    15. 14 6 22f

    16. 13b 12

    56

    Solve each inequality and graph the solutions.

    17. 5a 2 22

    18. 13 2t 3(t 3)

    4 28 6 2 4 6 8 0

    4 28 6 2 4 6 8 0

    b 4f 11

    r 2c 4

    4x 60; x 15; Each present will cost at least $15.

    4 28 6 2 4 6 8 0

    4 28 6 2 4 6 8 0

    4 28 6 2 4 6 8 0

    k 6;

    h 6;

    r 3;

    a 4;

    t 4;

    CHAPTER 3 REVIEW CONTINUED

  • Copyright by Holt, Rinehart and Winston. 47 Algebra 1All rights reserved.

    3-5 Solving Inequalities with Variables on Both Sides

    Solve each inequality.

    19. 12(3 8t) 20(1 15t) 20. 2(4 a) 2 2a 6

    Solve each inequality and graph the solutions.

    21. 4(3m 1) 2(m 3)

    22. 9d 4 12 5d

    23. The booster club raised $104 to buy soccer balls for the soccer team. Each soccer ball costs $19. How many soccer balls can the booster club buy?

    3-6 Solving Compound Inequalities

    Solve each compound inequality and graph the solutions.

    24. 4 r 5 1

    25. 4v 3 5 or 2v 7 1

    Write the compound inequality shown by each graph.

    26.

    27.4 2 2 40

    4 2 2 40

    CHAPTER 3 REVIEW CONTINUED

  • Copyright by Holt, Rinehart and Winston. 47 Algebra 1All rights reserved.

    3-5 Solving Inequalities with Variables on Both Sides

    Solve each inequality.

    19. 12(3 8t) 20(1 15t) 20. 2(4 a) 2 2a 6

    Solve each inequality and graph the solutions.

    21. 4(3m 1) 2(m 3)

    22. 9d 4 12 5d

    23. The booster club raised $104 to buy soccer balls for the soccer team. Each soccer ball costs $19. How many soccer balls can the booster club buy?

    3-6 Solving Compound Inequalities

    Solve each compound inequality and graph the solutions.

    24. 4 r 5 1

    25. 4v 3 5 or 2v 7 1

    Write the compound inequality shown by each graph.

    26.

    27.4 k 2

    4 2 2 40

    x 0 OR x 04 2 2 40

    4 28 6 2 4 6 8 0

    4 28 6 2 4 6 8 0

    They can buy no more than 5 soccer balls.

    4 28 6 2 4 6 8 0

    4 28 6 2 4 6 8 0

    all real numbersno solutions

    m 1;

    d 4;

    1 r 4;

    v 2 OR v 3;

    CHAPTER 3 REVIEW CONTINUED

  • Copyright by Holt, Rinehart and Winston. 48 Algebra 1All rights reserved.

    CHAPTER 3 REVIEW CONTINUED

    3-7 Solving Absolute-Value Inequalities

    Solve each inequality.

    28. x 3 5 29. 3a 9 2

    Solve each absolute-value inequality and graph the solutions.

    30. x 3 2 31. x 2 2.8 3.2

    Write an absolute-value inequality for each graph.

    32.

    33.

    Tell whether the given value of x is a solution of the inequality.

    34. x 4; x 6

    2 3 4 51012345

    2 3 4 51012345

  • Copyright by Holt, Rinehart and Winston. 48 Algebra 1All rights reserved.

    CHAPTER 3 REVIEW CONTINUED

    3-7 Solving Absolute-Value Inequalities

    Solve each inequality.

    28. x 3 5 29. 3a 9 2

    Solve each absolute-value inequality and graph the solutions.

    30. x 3 2 31. x 2 2.8 3.2

    Write an absolute-value inequality for each graph.

    32.

    33.

    Tell whether the given value of x is a solution of the inequality.

    34. x 4; x 6yes

    x 3.52 3 4 51012345

    x 12 3 4 51012345

    8 x 4x 1 OR x 5

    all real numbers

    0 1 2 31234567 4 6 8 1020246810

  • Big Ideas3

    CHAPTER

    Copyright by Holt, Rinehart and Winston. 49 Algebra 1All rights reserved.

    Answer these questions to summarize the important concepts fromChapter 3 in your own words.

    1. Explain how to show that an endpoint is a solution. Explain how to showthat an endpoint is not a solution.

    2. Explain how solving a one-step or multi-step inequality is like solving aone-step or multi-step equation.

    3. Explain how solving inequalities by multiplying or dividing by a negativenumber is different from solving inequalities by multiplying or dividing by apositive number.

    4. Explain how to graph a compound inequality involving a union

    5. Describe how to use an absolute-value inequality to find all the values on anumber line that are within 3 units of 1.

    For more review of Chapter 3: Complete the Chapter 3 Study Guide and Review on pages 186189 of

    your textbook. Complete the Ready to Go On quizzes on pages 155 and 185 of your

    textbook.

  • Big Ideas3

    CHAPTER

    Copyright by Holt, Rinehart and Winston. 49 Algebra 1All rights reserved.

    Answer these questions to summarize the important concepts fromChapter 3 in your own words.

    1. Explain how to show that an endpoint is a solution. Explain how to showthat an endpoint is not a solution.

    2. Explain how solving a one-step or multi-step inequality is like solving aone-step or multi-step equation.

    3. Explain how solving inequalities by multiplying or dividing by a negativenumber is different from solving inequalities by multiplying or dividing by apositive number.

    4. Explain how to graph a compound inequality involving a union

    5. Describe how to use an absolute-value inequality to find all the values on anumber line that are within 3 units of 1.

    For more review of Chapter 3: Complete the Chapter 3 Study Guide and Review on pages 186189 of

    your textbook. Complete the Ready to Go On quizzes on pages 155 and 185 of your

    textbook.

    The difference between a number and 1 must be less than 3.x (1) 3, or x 1 3

    Graph each part of the inequality separately noting when to use asolid circle and when to use an empty circle.

    When you multiply or divide both sides of an inequality by thesame negative number, you reverse the inequality symbol. Whenyou multiply or divide both sides of an inequality by the samepositive number, you do not change the inequality symbol.

    To solve an inequality or an equation, you need to isolate thevariable and use inverse operations.

    To show that an endpoint is a solution, draw a solid circle at thenumber. To show that an endpoint is not a solution, draw an emptycircle.