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Lesson 8-1 Solving Equations with Variables on Each Side Lesson 8-2 Solving Equations with Grouping Symbols Lesson 8-3 Inequalities Lesson 8-4 Solving Inequalities by Adding or Subtracting Lesson 8-5 Solving Inequalities by Multiplying or Dividing Lesson 8-6 Solving Multi-Step Inequalities Five-Minute Check (over Chapter 7) Main Idea Targeted TEKS Example 1: Equations with Variables on Each Side Example 2: Equations with Variables on Each Side Example 3: Real-World Example • Solve equations with variables on each side. 8.2 The student selects and uses appropriate operations to solve problems and justify solutions. (A) Select appropriate operations to solve problems involving rational numbers and justify the selections. (B) Use appropriate operations to solve problems involving rational numbers in problem situations. Also addresses TEKS 8.5(A). Equations with Variables on Each Side Solve 5x + 12 = 2x. Check your solution. 5x + 12 = 2x Write the equation. 5x – 5x + 12 = 2x – 5x Subtract 5x from each side. 12 = –3x Simplify. –4 = x Mentally divide each side by –3. Subtract 5x from Subtract 5x from the left side of the the right side of equation to isolate the equation to the variable. keep it balanced Equations with Variables on Each Side To check your solution, replace x with –4 in the original equation. Check 5x + 12 = 2x Write the equation. ? 5(–4) + 12 = 2(–4) Replace x with –4. ? –20 + 12 = –8 Simplify. –8 = –8 This statement is true. Answer: The solution is –4. BrainPOP: Two-Step Equations Solve 7x = 5x + 6. Check your solution. A. –3 B. C. 3 A. A B. 0% B D. 21 0% 0% 0% C. C A B C D D. D Equations with Variables on Each Side A. Solve 7x + 3 = 2x + 23. 7x + 3 = 2x + 23 Write the equation. 7x – 2x + 3 = 2x – 2x + 23 Subtract 2x from each side. 5x + 3 = 23 Simplify. 5x + 3 – 3 = 23 – 3 Subtract 3 from each side. 5x = 20 Simplify. x=4 Check your solution. Answer: The solution is 4. Equations with Variables on Each Side B. Solve 1.7 + a = 3.8a – 5.3. 1.7 + a = 3.8a – 5.3 Write the equation. 1.7 + a – a = 3.8a – a – 5.3 Subtract a from each side. 1.7 = 2.8a – 5.3 Simplify. 1.7 + 5.3 = 2.8a – 5.3 + 5.3 Add 5.3 to each side. 7.0 = 2.8a Simplify. Divide each side by 2.8. 2.5 = a Check your solution. Answer: The solution is 2.5 A. Solve 4x + 15 = 2x – 7. A. B. 0% 1. A C. –11 2. B 3. C D. –22 4. D A B C D B. Solve 2.4 – 3m = 6.4m – 8.88. A. 3.3 B. 1.2 0% 1. A C. –0.7 2. B 3. C D. –1.9 4. D A B C D CAR RENTAL A car rental agency has two plans. Under plan A, a car rents for $80 plus $20 each day. Under plan B, a car rents for $120 plus $15 each day. What number of days results in the same cost? Let d represent the number of days. $80 plus $20 for each day equals $120 plus $15 for each day 80 + 20d = 120 + 15d Write the original equation. 80 + 20d – 15d = 120 + 15d – 15d Subtract 15d from each side. 80 + 5d = 120 Simplify. 80 – 80 + 5d = 120 – 80 Subtract 80 from each side. 5d = 40 Simplify. Divide each side by 5. d= 8 Simplify. Answer: The cost would be the same for 8 days. CELL PHONES A cell phone provider offers two plans. Under plan A, the monthly cost is $20 with a cost of $0.35 per minute. Under plan B, the monthly cost is $35 with a cost of $0.15 per minute. What number of minutes results in the same cost? A. 30 minutes 0% 1. A B. 75 minutes 2. B 3. C C. 110 minutes 4. D D. 275 minutes A B C D Five-Minute Check (over Lesson 8-1) Main Ideas and Vocabulary Targeted TEKS Example 1: Solve Equations with Parentheses Example 2: Use an Equation to Solve a Problem Example 3: No Solution Example 4: All Numbers as Solutions • Solve equations that involve grouping symbols. • Identify equations that have no solution or an infinite number of solutions. • null or empty set • identity 8.2 The student selects and uses appropriate operations to solve problems and justify solutions. (A) Select appropriate operations to solve problems involving rational numbers and justify the selections. (B) Use appropriate operations to solve problems involving rational numbers in problem situations. Also addresses TEKS 8.5(A). Solve Equations with Parentheses A. Solve 3h = 5(h – 2). Check your solution. 3h = 5(h – 2) Write the equation. 3h = 5(h) – 5(2) Use the Distributive Property. 3h = 5h – 10 Simplify. 3h – 5h = 5h – 5h – 10 Subtract 5h from each side. –2h = –10 Simplify. Divide each side by –2. Solve Equations with Parentheses h =5 Simplify. Check 3h = 5(h – 2) Write the equation. ? 3(5) = 5(5 – 2) Replace h with 5. ? 15 = 5(3) Simplify. 15 = 15 This statement is true. Answer: The solution is 5. Solve Equations with Parentheses B. Solve 6(b – 2) = 3(b + 8.5). Check your solution. 6(b – 2) = 3(b + 8.5) Write the equation. 6b – 12 = 3b + 25.5 Use the Distributive Property. 6b – 12 – 3b = 3b – 3b + 25.5 Subtract 3b from each side. 3b – 12 = 25.5 Simplify. 3b – 12 + 12 = 25.5 + 12 Add 12 to each side. 3b = 37.5 Simplify. Divide each side by 3. Solve Equations with Parentheses b = 12.5 Simplify. Answer: The solution is 12.5. A. Solve 4t = 7(t – 3). Check your solution. A. –7 B. 1 C. A. A B. 0% B D. 7 0% 0% 0% C. C A B C D D. D B. Solve 3(p + 5) = 6(p – 2). Check your solution. A. 9 B. 8 C. A. A B. 0% B D. 0% 0% 0% C. C A B C D D. D Use an Equation to Solve a Problem GEOMETRY The perimeter of a rectangle is 36 inches. Find the dimensions if the length is 2 inches greater than three times the width. Words 2 times the length + 2 times the width = perimeter Variable Let w = the width. Let 3w + 2 = the length. w Equation 2(3w + 2) + 2w = 36 3w + 2 Use an Equation to Solve a Problem 2(3w + 2) + 2w = 36 Write the equation. 6w + 4 + 2w = 36 Use the Distributive Property. 8w + 4 = 36 Simplify. 8w + 4 – 4 = 36 – 4 Subtract 4 from each side. 8w = 32 Simplify. w =4 Mentally divide each side by 8. Evaluate 3w + 2 to find the length. 3(4) + 2 = 12 + 2 or 14 Replace w with 4. Answer: The width is 4 inches. The length is 14 inches. GEOMETRY The perimeter of a rectangle is 26 feet. Find the dimensions if the length is 2 feet less than twice the width. A. 0% B. 1. A C. width = 5 ft; length = 8 ft 2. B 3. C A B C D 4. D D. width = 11 ft; length = 24 ft No Solution Solve 4x – 0.3 = 4x + 0.9. 4x – 0.3 = 4x + 0.9 Write the equation. 4x – 4x – 0.3 = 4x – 4x + 0.9 Subtract 4x from each side. –0.3 = 0.9 Simplify. Answer: The sentence –0.3 = 0.9 is never true. So, the solution set is Ø. Interactive Lab: Solving Two-Step Equations Solve 16 + 1.3m = –12 + 1.3m. A. 3.1 0% B. 21.5 1. A C. The solution set is Ø. 2. B 3. C 4. D D. The solution set is all A B C D numbers. All Numbers as Solutions Solve 3(4x – 2) + 15 = 12x + 9. 3(4x – 2) + 15 = 12x + 9 Write the equation. 12x – 6 + 15 = 12x + 9 Use the Distributive Property. 12x + 9 = 12x + 9 Simplify. 12x + 9 – 9 = 12x + 9 – 9 Subtract 9 from each side. 12x = 12x Simplify. x =x Mentally divide each side by 12. Answer: The sentence x = x is always true. The solution set is all numbers. Solve 10a – 9 = 5(2a – 3) + 6. A. 0 B. C. The solution set is Ø. A. A B. 0% B D. The solution set is all 0% 0% 0% C. C numbers. A B C D D. D Five-Minute Check (over Lesson 8-2) Main Ideas and Vocabulary Targeted TEKS Example 1: Write Inequalities Key Concept: Inequalities Example 2: Real-World Example Example 3: Determine Truth of an Inequality Example 4: Graph Inequalities Example 5: Write an Inequality • Write inequalities. • Graph inequalities. • inequality 8.2 The student selects and uses appropriate operations to solve problems and justify solutions. (A) Select appropriate operations to solve problems involving rational numbers and justify the selections. (B) Use appropriate operations to solve problems involving rational numbers in problem situations. Also addresses TEKS 8.4(A). Write Inequalities A. Write an inequality for the following sentence. Your height is greater than 52 inches. Words Your height is greater than 52 inches. Variable Let h represent height. Inequality h > 52 Answer: h > 52 Write Inequalities B. Write an inequality for the following sentence. Your speed is less than or equal to 62 mph. Words Your speed is less than or equal to 62 mph. Variable Let s represent speed. Inequality s ≤ 62 Answer: s ≤ 62 A. Write an inequality for the following sentence. Your height is less than 48 inches. A. h < 48 B. h > 48 C. h ≤ 48 A. A 0% 0% B. 0% B 0% C. C D. h ≥ 48 A B C D D. D B. Write an inequality for the following sentence. Your age is greater than 12 years. A. a < 12 B. a > 12 C. a ≤ 12 A. A 0% 0% B. 0% B 0% C. C D. a ≥ 12 A B C D D. D ENVIRONMENT To meet a certain air quality standard, an automobile must have a fuel efficiency of not less than 27.5 miles per gallon. Write an inequality to describe this situation. Words Fuel efficiency of at least 27.5 miles per gallon Variable Let e = fuel efficiency in miles per gallon Inequality e ≥ 27.5 Answer: The inequality is e ≥ 27.5. CAFETERIA The school cafeteria allows each student no more than 2 servings of dessert during lunch. Write an inequality to describe this situation. A. s < 2 0% B. s > 2 1. A 2. B C. s ≤ 2 3. C 4. D A B C D D. s ≥ 2 Determine Truth of an Inequality A. For the given value, state whether the inequality is true or false. s – 9 < 4, s = 6 s–9 < 4 Write the inequality. ? 6–9<4 Replace s with 6. –3 < 4 Simplify. Answer: The sentence is true. Determine Truth of an Inequality B. For the given value, state whether the inequality is true or false. Write the inequality. Replace a with 36. ? 14 ≤ 12 + 1 Simplify. 14 ≤ 13 Simplify. Answer: The sentence is false. A. For the given value, state whether the inequality is true or false. 12 – m > 7, m = 5 A. true 0% B. false 1. A 2. B 3. C C. sometime true 4. D A B C D D. cannot be determined B. For the given value, state whether the inequality is true or false. 0% A. true 1. A B. false 2. B 3. C 4. D C. sometime true A B C D D. cannot be determined Graph Inequalities A. Graph x > 10 on a number line. Answer: The open circle means the number 10 is not included in the graph. Graph Inequalities B. Graph x ≥ 10 on a number line. Answer: The closed circle means the number 10 is included in the graph. Graph Inequalities C. Graph x < 10 on a number line. Answer: The open circle means the number 10 is not included in the graph. Graph Inequalities D. Graph x ≤ 10 on a number line. Answer: The closed circle means the number 10 is included in the graph. A. Graph x < 3 on a number line. A. B. C. A. A B. 0% B D. 0% 0% 0% C. C A B C D D. D B. Graph x > 3 on a number line. A. B. C. A. A B. 0% B D. 0% 0% 0% C. C A B C D D. D C. Graph x ≤ 3 on a number line. A. B. C. A. A B. 0% B D. 0% 0% 0% C. C A B C D D. D D. Graph x ≥ 3 on a number line. A. B. C. A. A B. 0% B D. 0% 0% 0% C. C A B C D D. D Write an Inequality Write the inequality for the graph. A closed circle is on –38, so the point –38 is included in the graph. The arrow points to the right, so the graph includes all numbers greater than or equal to –38. Answer: The inequality is x ≥ –38. Write the inequality for the graph. A. x < –7 B. x > –7 A. A B. 0% B C. x ≤ –7 0% 0% 0% C. C A B C D D. D D. x ≥ –7 Five-Minute Check (over Lesson 8-3) Main Idea Targeted TEKS Key Concept: Addition and Subtraction Properties Example 1: Solve an Inequality Using Subtraction Example 2: Solve an Inequality Using Addition Example 3: Graph Solutions of Inequalities Example 4: Real-World Example • Solve inequalities by using the Addition and Subtraction Properties of Inequality. 8.2 The student selects and uses appropriate operations to solve problems and justify solutions. (A) Select appropriate operations to solve problems involving rational numbers and justify the selections. (B) Use appropriate operations to solve problems involving rational numbers in problem situations. Also addresses TEKS 8.4(A). Solve an Inequality Using Subtraction Solve y + 5 > 11. Check your solution. y + 5 > 11 Write the inequality. y + 5 – 5 > 11 – 5 Subtract 5 from each side. y>6 Simplify. To check your solution, try any number greater than 6. Check y + 5 > 11 Write the inequality. ? 7 + 5 > 11 Replace y with 7. 12 > 11 This statement is true. Answer: The solution is y > 6. Solve x + 9 < 13. A. x < 22 B. x < 4 C. x < –4 A. A B. 0% B D. x > 4 0% 0% 0% C. C A B C D D. D Solve an Inequality Using Addition Solve –21 ≥ d – 8. Check your solution. –21 ≥ d – 8 Write the inequality. –21 + 8 ≥ d – 8 + 8 Add 8 to each side. –13 ≥ d Simplify. Answer: The solution is –13 ≥ d or d ≤ –13. Solve m + 8 < –2. Check your solution. A. m > 10 B. m < 6 0% 1. A C. m < –6 2. B 3. C D. m < –10 4. D A B C D Graph Solutions of Inequalities Solve Graph the solution on a number line. Write the inequality. Graph Solutions of Inequalities Simplify. Answer: Graph the solution. Answer: Solve Graph the solution on a number line. A. 0% B. 1. A C. 2. B 3. C A B C D D. 4. D BOWLING Katya took $12 to the bowling alley. Shoe rental costs $3.75. What is the most she can spend on games and snacks? Explore We need to find the greatest amount Katya can spend on games and snacks. Plan Let x represent the amount Katya can spend on games and snacks. Write an inequality to represent the problem. Recall that at most means less than or equal to. Words Cost of shoes plus cost of games and snacks must be less than or equal to total. Variable Let x equal the cost of games and snacks. Inequality 3.75 + x ≤ 12 Solve 3.75 + x ≤ 12 Write the inequality. 3.75 – 3.75 + x ≤ 12 – 3.75 Subtract 3.75 from each side. x ≤ 8.25 Simplify. Check Check by choosing an amount less than or equal to $8.25, say, $6. Then Katya would spend $3.75 + $6 or $9.75 in all. Since $9.75 < $12, the answer is reasonable. Answer: The most Katya can spend on games and snacks is $8.25. MOVIES Danielle has $10 to take to the movies. If the cost of a ticket is $4.50, what is the most she can spend on snacks? A. $5.50 B. $6.00 A. A C. $6.50 0% 0% B. 0% B 0% C. C A B C D D. $14.50 D. D Five-Minute Check (over Lesson 8-4) Main Ideas Targeted TEKS Key Concept: Multiplication and Division Properties Example 1: Multiply or Divide by a Positive Number Example 2: Test Example Key Concept: Multiplication and Division Properties Example 3: Multiply or Divide by a Negative Number • Solve inequalities by multiplying and dividing by a positive number. • Solve inequalities by multiplying or dividing by a negative number. 8.2 The student selects and uses appropriate operations to solve problems and justify solutions. (A) Select appropriate operations to solve problems involving rational numbers and justify the selections. (B) Use appropriate operations to solve problems involving rational numbers in problem situations. Also addresses TEKS 8.4(A). Multiply or Divide by a Positive Number A. Solve 9x ≤ 54. Check your solution. 9x ≤ 54 Write the inequality. Divide each side by 9. x≤6 Simplify. Answer: The solution is x ≤ 6. You can check this solution by substituting 6 or a number less than 6 into the inequality. Multiply or Divide by a Positive Number B. Solve Check your solution. Write the inequality. Multiply each side by 9. d > 36 Simplify. Answer: The solution is d > 36. You can check this solution by substituting 36 or a number greater than 36 into the inequality. A. Solve 3y > 21. Check your solution. A. y > 63 B. y > 7 C. y < 18 A. A B. 0% B D. y < 7 0% 0% 0% C. C A B C D D. D B. Solve Check your solution. A. p ≥ 2 B. p ≥ 3 C. p ≥ 18 A. A B. 0% B D. p ≤ 18 0% 0% 0% C. C A B C D D. D Martha earns $9 per hour working at a fast food restaurant. Which inequality can be used to find how many hours she must work in a week to earn at least $117? A 9x < 117 B 9x ≥ 117 C 9x > 117 D 9x ≤ 117 Read the Test Item You are to write an inequality to represent a real-world problem. Solve the Test Item Words Amount earned per hour times number of hours is at least amount earned each week. Variable Let x represent the number of hours worked. Inequality 9 ● x ≥ 117 Answer: The answer is B. TEST EXAMPLE Ed earns $6 per hour working at the library. Which inequality can be used to find how many hours he must work in a week to earn more than $100? A. 6x < 100 0% B. 6x ≥ 100 1. A 2. B C. 6x ≤ 100 3. C 4. D D. 6x > 100 A B C D Multiply or Divide by a Negative Number A. Solve and check your solution. Then graph the solution on a number line. Write the inequality. Multiply each side by –5 and reverse the symbol. Answer: x ≤ –35 Check this result. Graph the solution x ≤ –35. Multiply or Divide by a Negative Number B. Solve –9x < –27 and check your solution. Then graph the solution on a number line. –9x < –27 Write the inequality. Divide each side by –9 and reverse the symbol. Answer: x > 3 Check this result. Graph the solution, x > 3. A. Solve and check your solution. Then graph your solution on a number line. A. x < 18 0% B. x < –2 1. A 2. B C. x < –18 3. A C B C D 4. D D. x > –18 B. Solve –5x ≤ –40 and check your solution. Then graph your solution on a number line. A. x ≥ –45 0% B. x ≥ –8 1. A 2. B C. x ≤ 8 3. A C B C D 4. D D. x ≥ 8 Five-Minute Check (over Lesson 8-5) Main Idea Targeted TEKS Example 1: Solve a Two-Step Inequality Example 2: Reverse the Inequality Symbol Example 3: Real-World Example • Solve inequalities that involve more than one operation. 8.2 The student selects and uses appropriate operations to solve problems and justify solutions. (A) Select appropriate operations to solve problems involving rational numbers and justify the selections. (B) Use appropriate operations to solve problems involving rational numbers in problem situations. Also addresses TEKS 8.4(A). Solve a Two-Step Inequality Solve 5x + 13 > 83 and check your solution. Graph the solution on a number line. 5x + 13 > 83 Write the inequality. 5x + 13 – 13 > 83 – 13 Subtract 13 from each side. 5x > 70 Simplify. Divide each side by 5. Answer: x > 14 Simplify. BrainPOP: Solving Inequalities Solve a Two-Step Inequality Check 5x + 13 > 18 Write the inequality. ? 5(15) + 13 > 83 Replace x with a number greater than 14. Try 15. ? 75 + 13 > 83 Simplify. 88 > 83 The solution checks. Graph the solution, x > 14. Answer: x > 14 Solve 3x – 9 < 18 and check your solution. Graph the solution on a number line. A. x < 3 B. x < 9 C. x > 3 A. A 0% 0% B. 0% B 0% C. C D. x > 9 A B C D D. D Reverse the Inequality Symbol Solve 7 – 4a ≤ 23 – 2a and check your solution. Graph the solution. 7 – 4a ≤ 23 – 2a Write the inequality. 7 – 4a + 2a ≤ 23 – 2a + 2a Add 2a to each side. 7 – 2a ≤ 23 Simplify. 7 – 7 – 2a ≤ 23 – 7 Subtract 7 from each side. –2a ≤ 16 Simplify. Divide each side by –2 and change ≤ to ≥. Answer: a ≥ –8 Simplify. Reverse the Inequality Symbol Check your solution by substituting a number greater than or equal to –8. Graph the solution, a ≥ –8. Answer: Solve 8 + 2x < 5x – 7 and check your solution. Graph the solution on a number line. A. x > 5 0% B. x < 5 1. A 2. B C. 3. C A B C D 4. D D. RUNNING José wants to run a 10k marathon. Refer to Get Ready for the Lesson. If the length of his current daily run is 2 kilometers, how many kilometers should he increase his daily run to have enough endurance for the race? Words 3 times 2 plus amount of increase is greater than or equal to desired distance Variable Let d = the amount of increase. Inequality 3 (2 + d) ≥ 10 3(2 + d) ≥ 10 Write the inequality. 6 + 3d ≥ 10 Use the Distributive Property. 6 + 3d – 6 ≥ 10 – 6 Subtract 6 from each side. 3d ≥ 4 Simplify. Divide each side by 3. Simplify. Answer: At least km BACKPACKING A person weighing 168 pounds has a 7-pound backpack. If three times the weight of your backpack and its contents should be less than your body weight, what is the maximum weight for the contents of the pack? 0% A. greater than 49 pounds 1. A B. less than 49 pounds 2. B 3. C C. 4. D A B C D D. less than 147 pounds Five-Minute Checks Image Bank Math Tools Solving Two-Step Equations Two-Step Equations Solving Inequalities Lesson 8-1 (over Chapter 7) Lesson 8-2 (over Lesson 8-1) Lesson 8-3 (over Lesson 8-2) Lesson 8-4 (over Lesson 8-3) Lesson 8-5 (over Lesson 8-4) Lesson 8-6 (over Lesson 8-5) To use the images that are on the following three slides in your own presentation: 1. Exit this presentation. 2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides. 3. Select an image, copy it, and paste it into your presentation. (over Chapter 7) Which of the following options correctly states and explains whether the given relation is a function? {(–1, 2), (0, 1), (2, 1), (0, 2)} A. No; 0 is paired with 1 and 2. B. No; –1 is paired with –2 and 0. A. A C. Yes; there is no many-to- one relation present. 0% 0% B. 0% B 0% C. C D. Yes; there is no one-to- A B C D D. D many relation present. (over Chapter 7) Find the x-intercept and y-intercept for the graph of 2x + y = 6. A. 2, 1 0% B. 3, 1 1. A 2. B C. 2, 6 3. C 4. D A B C D D. 3, 6 (over Chapter 7) Find the slope of the line that passes through the pair of points A(4, 2) and B(–4, –4). A. 0% B. 1. A 2. B 3. C C. 0 4. D A B C D D. undefined (over Chapter 7) State the slope and the y-intercept for the graph of the equation x + 2y = –8. A. B. C. –2, –4 A. A 0% 0% B. 0% B 0% C. C D. –4, –2 A B C D D. D (over Chapter 7) Which ordered pair is not a solution of A. (1, –1) B. (–2, –5) 0% 1. A C. (–2, –3) 2. B 3. C 4. D D. (–1, –1) A B C D (over Lesson 8-1) Solve 2x + 15 = 7x. A. –3 B. C. A. A 0% 0% B. 0% B 0% D. 3 C. C A B C D D. D (over Lesson 8-1) Solve 5a = 3a – 18. A. –9 B. 0% 1. A C. 2. B 3. C 4. D D. A B C D (over Lesson 8-1) Solve 1.3 – 3b = b – 0.3. A. 1.4 0% B. 1.04 1. A 2. B C. 0.4 3. C 4. D D. 0.14 A B C D (over Lesson 8-1) Solve 4x – 7 = –5x – 25. A. –18 B. –2 C. A. A 0% 0% B. 0% B 0% D. C. C A B C D D. D (over Lesson 8-1) Solve 7.5 + n = 2.7n – 1. A. 5 B. 4 0% 1. A C. –4.8 2. B 3. C 4. D D. –5.8 A B C D (over Lesson 8-1) What is the solution of 6 – 2a = 2a – 6? A. –3 0% B. –1 1. A 2. B C. 0 3. C 4. D D. 3 A B C D (over Lesson 8-2) Solve 2(x – 5) = 8. A. 13 B. 9 C. 6.5 A. A 0% 0% B. 0% B 0% D. 4.5 C. C A B C D D. D (over Lesson 8-2) Solve 3(2a – 1) = 42. A. 6.8 B. 7.1 0% 1. A C. 7.3 2. B 3. C 4. D D. 7.5 A B C D (over Lesson 8-2) Solve 6(n – 4) = 3(n + 3). A. 11 0% B. 2.3 1. A 2. B C. –2.5 3. C 4. D D. –5 A B C D (over Lesson 8-2) Solve 5(x – 4) = 2(x – 2.5). A. 1 B. 2.1 C. 5 A. A 0% 0% B. 0% B 0% D. 8.3 C. C A B C D D. D (over Lesson 8-2) Find the dimensions of the rectangle shown in the figure. The perimeter is 90 meters. A. w = 8 m; ℓ = 27 m 0% B. w = 9 m; ℓ = 31 m 1. A 2. B C. w = 19 m; ℓ = 71 m 3. C 4. D A B C D D. w = 10 m; ℓ = 35 m (over Lesson 8-2) Which equation has no solution? A. 12n – 6 = 2(n + 1) 0% B. 8n – 7 = 5(n – 5) 1. A 2. B C. 5(n + 4) + 8 = 5n + 20 3. C 4. D D. 4(2n + 6) = 4(n + 3) A B C D (over Lesson 8-3) Write an inequality for the sentence. A number decreased by 7 is at most 9. A. n – 7 > 9 B. n – 7 < 9 C. A. A 0% 0% B. 0% B 0% C. C D. A B C D D. D (over Lesson 8-3) Write an inequality for the sentence. There are more than 500 students (s) at Candlewood Middle School. A. s > 500 0% B. s < 500 1. A 2. B C. 3. C 4. D A B C D D. (over Lesson 8-3) For n = 4, state whether the inequality 15 – n < 9 is true or false. A. true 0% 0% B. false A B 1. A 2. B (over Lesson 8-3) For a = 7, state whether the inequality 6a ≥ 42 is true or false. A. true 0% 0% B. false A B 1. A 2. B (over Lesson 8-3) Write the inequality for the graph. A. x < –2 0% B. 1. A 2. B C. x > –2 3. C 4. D A B C D D. (over Lesson 8-3) If Mike collects 3 more model planes, he will have at least 10 model planes. Which inequality represents this situation? A. p + 3 > 10 0% 1. A B. p + 3 < 10 2. B 3. C C. 4. D A B C D D. (over Lesson 8-4) Solve the inequality k + 5 > –2. A. k > –7 B. k < –7 C. k > 7 A. A 0% 0% B. 0% B 0% D. k < 7 C. C A B C D D. D (over Lesson 8-4) Solve the inequality A. B. 0% 1. A C. 2. B 3. C 4. D D. A B C D (over Lesson 8-4) Solve the inequality A. 0% B. 1. A 2. B C. 3. C 4. D D. A B C D (over Lesson 8-4) A. B. C. A. A 0% 0% B. 0% B 0% D. C. C A B C D D. D (over Lesson 8-4) Solve the inequality –8 < x – (–4). A. x > 12 B. x < 12 0% 1. A C. x < –12 2. B 3. C 4. D D. x > –12 A B C D (over Lesson 8-4) Tina can spend $20 at most on 2 birthday presents. If she spends $9.50 on one present, which inequality represents all the possible amounts p that she can spend on other presents? A. 0% 1. A B. 2. B 3. C C. 4. D D. A B C D (over Lesson 8-5) Solve the inequality 2x > 22. A. x > 11 B. x > 20 C. x < 11 A. A 0% 0% B. 0% B 0% D. x < 20 C. C A B C D D. D (over Lesson 8-5) Solve the inequality A. B. 0% 1. A C. 2. B 3. C 4. D D. A B C D (over Lesson 8-5) Solve the inequality A. 0% B. 1. A 2. B C. 3. C 4. D D. A B C D (over Lesson 8-5) Solve the inequality 0.8r < –24. A. r < –30 B. r > –30 C. r < –0.3 A. A 0% 0% B. 0% B 0% D. r > –0.3 C. C A B C D D. D (over Lesson 8-5) A. B. 0% 1. A C. 2. B 3. C 4. D D. A B C D (over Lesson 8-5) The product of an integer and –9 is less than –45. Find the least integer that meets this condition. A. –6 0% B. –5 1. A 2. B 3. C C. 5 4. D D. 6 A B C D This slide is intentionally blank.