Inequalities Study Guide
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1 Class: Date: Inequalities Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. Which number is a solution of the inequality? m > 8 a. I don t know. d. b. 0 e. 11 c. 9 Write the inequality in words. 2. n < 52 a. fifty-two less than three times n b. Three times n is less than fifty-two. c. Three times n is less than or equal to fifty-two. d. Three times n is greater than fifty-two. e. I don t know.. 5n 10 > 26 a. Five times n less than ten is twenty-six. b. Ten plus five times a number is less than or equal to twenty-six. c. Ten less than five times a number is greater than twenty-six. d. Ten less than a number is less than or equal to twenty-six. e. I don t know. 4. p < Graph the inequality. a. d. b. I don t know. e. c. 1
2 5. a > 9 2 a. d. I don t know. b. e. c x a. d. b. I don t know. e. c. Write an inequality for the graph. 7. a. I don t know. d. x b. x < e. x < c. x > 8. Tina can type at least 40 words per minute. Write and graph an inequality to model this situation. a. I don t know. d. t 40 b. t> 40 e. t 40 c. t< 40 Write an inequality to model the situation. 9. Thomas earned $66 or more. a. t > 66 d. t 66 b. t 66 e. I don t know. c. t < 66 2
3 10. A number exceeds 48. a. I don t know. d. n 48 b. n > 48 e. n < 48 c. n 48 Solve the inequality. Then graph your solution. 11. x 1 5 a. I don t know. d. x 5 1 b. x 4 e. x 6 c. x y 5 a. y 45 d. y 45 b. y e. y ³ x 6 a. x 18 d. I don t know. b. x 9 e. x 18 c. x 9
4 14. x 12 a. x 4 d. x 4 b. x> 15 e. x q < 15 a. q < d. q > b. q < 10 e. q > x 4 < 2 a. 2 x< 5 d. 2 x< 4 b. 0 x< 1 e. 0 x< < 2x 2 < 6 a. I don t know. d. 16 < x < 6 b. 7 < x < 4 e. 20 < x < 2 c. 9 < x < 2 4
5 18. d a. d 4 or d 4 d. d 8 or d 4 b. d 8 or d 4 e. I don t know. c. d 8 or d x+ 10 < 16 a. 1 > x > d. 1 < x < b. < x < e. 28 < x < The French club is sponsoring a bake sale. If their goal is to raise at least $ 110, how many pastries must they sell at $2.50 each in order to meet that goal? Write and solve an inequality. a. 2.50p 110; p 44 d. I don t know. b. 2.50p 110; p 275 e. 110p 2.50; p 44 c. 2.50p 110; p Write a compound inequality that the graph could represent. a. 2 x< 4 d. 4 x< 2 b. 4<x 2 e. I don t know. c. x 4 or x < 2 a. I don t know. d. r< 2 or r 5 b. r> 5 or r 2 e. r< 5 or r 2 c. 2 r < 5 5
6 2. A student scored 78 and 97 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 80 and 90, inclusive. a. I don t know b n 90; 7.5 n n c ; 65 n n d ; 95 n n e ; 57 n 9 Solve the compound inequality. Graph your solution x 8 < 10 or 4x + 2 > 14 a. x < 1 or x > d. x < 4 or x > 8 b. x < 1 or x > 4 e. I don t know. c. x < 9 or x > 4 Other 25. Are the solutions of the compound inequality x < OR x > 6 different from the solutions to the compound inequality x < AND x > 6? Explain. 6
7 Inequalities Study Guide Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: L2 REF: 4-1 Inequalities and Their Graphs OBJ: Identifying Solutions of Inequalities NAT: NAEP 2005 Aa ADP J..1 STA: 8NJ 4.5.E.1d TOP: 4-1 Example 1 KEY: solution of the inequality inequality 2. ANS: B PTS: 1 DIF: L REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d KEY: translating an inequality inequality. ANS: C PTS: 1 DIF: L REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d KEY: translating an inequality inequality 4. ANS: C PTS: 1 DIF: L2 REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d TOP: 4-1 Example KEY: graphing inequality 5. ANS: C PTS: 1 DIF: L2 REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d TOP: 4-1 Example KEY: graphing inequality 6. ANS: E PTS: 1 DIF: L2 REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d TOP: 4-1 Example KEY: graphing inequality 7. ANS: B PTS: 1 DIF: L2 REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d TOP: 4-1 Example 4 KEY: writing an inequality from a graph graphing 8. ANS: E PTS: 1 DIF: L REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d TOP: 4-1 Example 5 KEY: translating an inequality word problem problem solving 9. ANS: D PTS: 1 DIF: L REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d TOP: 4-1 Example 5 KEY: modeling with inequalities translating an inequality 10. ANS: B PTS: 1 DIF: L2 REF: 4-1 Inequalities and Their Graphs STA: 8NJ 4.5.E.1d KEY: modeling with inequalities translating an inequality 1
8 11. ANS: B PTS: 1 DIF: L2 REF: 4-2 Solving Inequalities Using Addition and Subtraction OBJ: Using Addition to Solve Inequalities NAT: NAEP 2005 N5e NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: 8NJ 4.5.D.4 NJ D.2a 8NJ 4.5.E.1d TOP: 4-2 Example 1 KEY: Addition Property of Inequality solving inequalities graphing 12. ANS: A PTS: 1 DIF: L REF: 4- Solving Inequalities Using Multiplication and Division OBJ: 4-.1 Using Multiplication to Solve Inequalities NAT: NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: NJ D.2a 8NJ 4.5.D.4 8NJ 4.5.E.1d NJ D.2a TOP: 4- Example 2 KEY: Multiplication Property of Inequality for c < 0 solving inequalities 1. ANS: A PTS: 1 DIF: L2 REF: 4- Solving Inequalities Using Multiplication and Division OBJ: 4-.1 Using Multiplication to Solve Inequalities NAT: NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: NJ D.2a 8NJ 4.5.D.4 8NJ 4.5.E.1d NJ D.2a TOP: 4- Example 1 KEY: Multiplication Property of Inequality for c > 0 solving inequalities 14. ANS: D PTS: 1 DIF: L2 REF: 4- Solving Inequalities Using Multiplication and Division OBJ: 4-.2 Using Division to Solve Inequalities NAT: NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: NJ D.2a 8NJ 4.5.D.4 8NJ 4.5.E.1d NJ D.2a TOP: 4- Example KEY: Division Property of Inequality solving inequalities 15. ANS: D PTS: 1 DIF: L2 REF: 4- Solving Inequalities Using Multiplication and Division OBJ: 4-.2 Using Division to Solve Inequalities NAT: NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: NJ D.2a 8NJ 4.5.D.4 8NJ 4.5.E.1d NJ D.2a TOP: 4- Example KEY: Division Property of Inequality graphing solving inequalities 16. ANS: E PTS: 1 DIF: L2 REF: 4-5 Compound Inequalities OBJ: Solving Compound Inequalities Containing And TOP: 4-5 Example 2 KEY: solving a compound inequality containing AND compound inequality 17. ANS: B PTS: 1 DIF: L2 REF: 4-5 Compound Inequalities OBJ: Solving Compound Inequalities Containing And TOP: 4-5 Example 2 KEY: solving a compound inequality containing AND compound inequality 18. ANS: D PTS: 1 DIF: L REF: 4-6 Absolute Value Equations and Inequalities OBJ: Solving Absolute Value Inequalities NAT: NAEP 2005 N1g NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: 8NJ 4.5.E.1d NJ D.2a NJ C.1c TOP: 4-6 Example KEY: solving absolute value inequalities graphing solving a compound inequality containing OR 2
9 19. ANS: D PTS: 1 DIF: L REF: 4-6 Absolute Value Equations and Inequalities OBJ: Solving Absolute Value Inequalities NAT: NAEP 2005 N1g NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: 8NJ 4.5.E.1d NJ D.2a NJ C.1c TOP: 4-6 Example KEY: solving absolute value inequalities graphing solving a compound inequality containing AND 20. ANS: A PTS: 1 DIF: L REF: 4- Solving Inequalities Using Multiplication and Division OBJ: 4-.2 Using Division to Solve Inequalities NAT: NAEP 2005 A4a NAEP 2005 A4c ADP J..1 STA: NJ D.2a 8NJ 4.5.D.4 8NJ 4.5.E.1d NJ D.2a TOP: 4- Example 4 KEY: Division Property of Inequality problem solving word problem solving inequalities 21. ANS: D PTS: 1 DIF: L REF: 4-5 Compound Inequalities OBJ: Solving Compound Inequalities Containing And TOP: 4-5 Example 4 KEY: writing a compound inequality compound inequality 22. ANS: E PTS: 1 DIF: L REF: 4-5 Compound Inequalities OBJ: Solving Compound Inequalities Joined by Or TOP: 4-5 Example 4 KEY: writing a compound inequality compound inequality 2. ANS: C PTS: 1 DIF: L REF: 4-5 Compound Inequalities OBJ: Solving Compound Inequalities Containing And TOP: 4-5 Example KEY: solving inequalities problem solving word problem solving a compound inequality containing AND 24. ANS: A PTS: 1 DIF: L2 REF: 4-5 Compound Inequalities OBJ: Solving Compound Inequalities Joined by Or TOP: 4-5 Example 5 KEY: solving a compound inequality containing OR graphing compound inequality OTHER 25. ANS: The solution to x < OR x > 6 is all numbers less than or greater than 6. There is no solution to x < AND x > 6 since a number cannot be less than and greater than 6 at the same time. PTS: 1 DIF: L REF: 4-5 Compound Inequalities OBJ: Solving Compound Inequalities Joined by Or TOP: 4-5 Example 5 KEY: solving a compound inequality containing OR reasoning writing in math
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