Unit 1 - Review (Equations and Inequalities)
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1 Name: Class: Date: ID: A Unit 1 - Review (Equations and Inequalities) Multiple Choice Identify the choice that best completes the statement or answers the question. What is the solution of the following one-step equation? 1. x! 0.7 =!2 a. 1.3 b. 0.4 c d Solve the equation. 2. 3y + 20 = 3 + 2y a.! 1 17 b c. 23 d.! r! r = r a b c. 0.5 d !5y! 9 =!(y! 1) a.! 1 2 b.!2 1 2 c.!2 d.! 2 5 Use an algebraic equation to solve the problem. 5. A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary. a. 7.5 cm by 22.5 cm c. 20 cm by 60 cm b. 7.5 cm by 52.5 cm d. 15 cm by 22.5 cm 6. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm? a cm, 11.5 cm, and 12.5 cm c. 7.5 cm, 11.5 cm, and 32.1 cm b cm, 30 cm, and 37.5 cm d cm, 25.7 cm, and 32.1 cm 7. Two cars leave Denver at the same time and travel in opposite directions. One car travels 10 mi/h faster than the other car. The cars are 300 mi apart in 3 h. How fast is each car traveling? a. 35 mi/h and 45 mi/h c. 45 mi/h and 55 mi/h b. 55 mi/h and 35 mi/h d. 55 mi/h and 65 mi/h 1
2 Name: ID: A Is the following always, sometimes, or never true? x! 7 = 7x + 7! 4x a. always b. sometimes c. never x! 10 = 10x + 11! 4x a. always b. sometimes c. never Solve the equation or formula for the indicated variable. 10. S = 5r 2 t, for t a. t = S 5! r b. t = 25r S c. t = r 2! 5S d. t = S 5r T = 4U E, for U a. U = T! E 4 b. U = T + E 4 c. U = 4T! E d. U = TE 4 What inequality represents the sentence? fewer than a number is at least 8 a. x + 14 "!8 c. 14! x #!8 b. x! 14 #!8 d. x! 14 <!8 13. The product of a number and 12 is no more than k " 8 a. 12n < 15 c. 12n # 15 b. 12n > 15 d. 12n " 15 Solve the inequality. Graph the solution set. a. k # 3 c. k " 3 b. k " 5 d. k # 5 2
3 Name: ID: A 15. 2r 9 # 6 a. r " c. r # b. r #!7 1 2 d. r "! b # 2(3b + 4) a. all real numbers c. b # b. b " d. no solutions Solve the problem by writing an inequality. 17. A club decides to sell T-shirts for $15 as a fund-raiser. It costs $20 plus $9 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $150. a. 15x! ( 9x + 20) # 150; x # c. (8x + 20)! 15x # 150; x # 20 b. 15x! 9x + 20 # 150; x # 20 d. 15x! 9(x + 20) # 150; x # If the perimeter of a rectangular picture frame must be less than 200 in., and the width is 36 in., what must the height h of the frame be? a. h < 64 in. b. h > 128 in. c. h > 64 in. d. h < 128 in. Is the inequality sometimes, always, or never true? 19.!2(2x + 9) >!4x + 9 a. always b. sometimes c. never 3
4 Name: ID: A 20. 2(10x! 5)! 9x " 11x + 13 a. always b. sometimes c. never Solve the compound inequality. Write your solution in interval notation x 5 < 17 or 5x + 6 > 31 a. x < 3 or x > 5 c. x < 3 or x > b. x <!5 1 2 or x > d. x <!5 1 2 or x > 5 22.!2 " 2x! 4 < 4 a. 0 " x <! 2 c. 1 " x < 0 b. 1 " x < 4 d. 3 " x < 6 Solve the absolute value equation. Graph the solution. 23. x! 3 = 1 a. x = 4 or x = 2 c. x =!2 or x = 1 3 b. x =!2 or x = 2 d. x =!2 or x = x! 5! 2 =!4 a. x = 3 8 or x = 1 c. x = 3 8 or x = b. x = 1 or x = d. x = 3 8 or x =
5 Name: ID: A 25. 4x + 1 =!3 a. x =! 1 2 or x = 1 2 c. x =!1 or x = 1 2 b. x =! 1 2 or x =!1 d. x =! 1 2 or x =! x = 10 a. x = 1 4 or x =!2 1 3 c. x = 1 4 or x =! b. x = 1 4 or x =!1 d. x =!1 or x =!2 1 3 Solve the inequality. Graph the solution x + 3 # 19 a. x "!22 or x # 16 c. x "!11 or x # 8 b. x "!8 or x # 8 d. x #!11 or x " x + 10 " 26 a. 18 # x # 8 c. 36 " x " 16 b. 18 " x " 8 d. x "! 8 or x # 8 5
6 Name: ID: A 29. 4x + 8 > 28 a. x <!36 or x > 20 c. x <!9 or x > 5 b. x >!9 or x < 5 d. x <!5 or x > A furniture maker uses the specification " w " for the width w in inches of a desk drawer. Write the specification as an absolute value inequality. a. w! 0.24 " c. w! 22 " 0.24 b. w! 0.12 " 22 d. w! 22 " When Spheres-R-Us ships bags of golf balls, the number of balls in each bag must be within 6 balls of 300. Write a compound inequality and an absolute value inequality for an acceptable number of golf balls b in each bag. a. 294 " b " 306; b! 6 " 300 c. 297 " b " 303; b! 300 " 6 b. 297 " b " 303; b! 3 " 300 d. 294 " b " 306; b! 300 " 6 Short Answer Solve the compound inequality. Write your solution in interval notation x + 10 # 10 and 7x 7 " 14 Solve the inequality. Graph the solution x < 9 6
7 ID: A Unit 1 - Review (Equations and Inequalities) Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 2 Solving a Multi-Step Equation KEY: equation solution of an equation inverse operations DOK: DOK 1 2. ANS: D PTS: 1 DIF: L2 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 2 Solving a Multi-Step Equation KEY: equation solution of an equation inverse operations DOK: DOK 1 3. ANS: C PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 2 Solving a Multi-Step Equation KEY: equation solution of an equation inverse operations DOK: DOK 1 4. ANS: B PTS: 1 DIF: L2 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 2 Solving a Multi-Step Equation KEY: equation solution of an equation inverse operations DOK: DOK 1 5. ANS: A PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve problems by writing equations TOP: 1-4 Problem 3 Using an Equation to Solve a Problem KEY: equation solution of an equation 6. ANS: B PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve problems by writing equations TOP: 1-4 Problem 3 Using an Equation to Solve a Problem KEY: equation solution of an equation 7. ANS: C PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve problems by writing equations TOP: 1-4 Problem 3 Using an Equation to Solve a Problem KEY: equation solution of an equation 8. ANS: A PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 4 Equations with No Solutions and Identities KEY: equation identity DOK: DOK 1 9. ANS: C PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 4 Equations with No Solutions and Identities KEY: equation DOK: DOK ANS: D PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 5 Solving a Literal Equation KEY: equation literal equation 11. ANS: D PTS: 1 DIF: L3 REF: 1-4 Solving Equations OBJ: To solve equations TOP: 1-4 Problem 5 Solving a Literal Equation KEY: equation literal equation 12. ANS: B PTS: 1 DIF: L2 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 1 Writing an Inequality from a Sentence KEY: compound inequality word problem problem solving DOK: DOK 1 1
8 ID: A 13. ANS: D PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 1 Writing an Inequality from a Sentence KEY: compound inequality word problem problem solving DOK: DOK ANS: C PTS: 1 DIF: L2 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 2 Solving and Graphing an Inequality 15. ANS: C PTS: 1 DIF: L2 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 2 Solving and Graphing an Inequality 16. ANS: A PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 2 Solving and Graphing an Inequality 17. ANS: A PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 3 Using an Inequality 18. ANS: A PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 3 Using an Inequality 19. ANS: C PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 4 No Solution or All Real Numbers as Solution 20. ANS: A PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities TOP: 1-5 Problem 4 No Solution or All Real Numbers as Solution 21. ANS: A PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities OBJ: To write and solve compound inequalities TOP: 1-5 Problem 6 Solving an OR Inequality KEY: compound inequality 22. ANS: B PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities OBJ: To write and solve compound inequalities TOP: 1-5 Problem 5 Solving an AND Inequality KEY: compound inequality 23. ANS: A PTS: 1 DIF: L2 TOP: 1-6 Problem 1 Solving an Absolute Value Equation KEY: absolute value DOK: DOK ANS: B PTS: 1 DIF: L2 TOP: 1-6 Problem 2 Solving a Multi-Step Absolute Value Equation KEY: absolute value DOK: DOK 1 2
9 ID: A 25. ANS: C PTS: 1 DIF: L3 TOP: 1-6 Problem 1 Solving an Absolute Value Equation KEY: absolute value DOK: DOK ANS: D PTS: 1 DIF: L3 TOP: 1-6 Problem 2 Solving a Multi-Step Absolute Value Equation KEY: absolute value DOK: DOK ANS: C PTS: 1 DIF: L3 TOP: 1-6 Problem 5 Solving the Absolute Value Inequality; "greater than" KEY: absolute value 28. ANS: B PTS: 1 DIF: L3 TOP: 1-6 Problem 4 Solving the Absolute Value Inequality; "less than" KEY: absolute value 29. ANS: C PTS: 1 DIF: L3 TOP: 1-6 Problem 5 Solving the Absolute Value Inequality; "greater than" KEY: absolute value 30. ANS: D PTS: 1 DIF: L3 TOP: 1-6 Problem 6 Using an Absolute Value Inequality KEY: absolute value 31. ANS: D PTS: 1 DIF: L3 TOP: 1-6 Problem 6 Using an Absolute Value Inequality KEY: absolute value SHORT ANSWER 32. ANS: x # 0 and x " 3 PTS: 1 DIF: L3 REF: 1-5 Solving Inequalities OBJ: To write and solve compound inequalities TOP: 1-5 Problem 5 Solving an AND Inequality KEY: compound inequality 3
10 ID: A 33. ANS:!4 3 4 < x < PTS: 1 DIF: L4 TOP: 1-6 Problem 4 Solving the Absolute Value Inequality; "less than" KEY: absolute value 4
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