Fair Game Review. Chapter inches. Your friend s height is 5.6 feet. Who is taller? Explain.

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1 Name Date Chapter 8 Fair Game Review Complete the number sentence with <, >, or = Your height is 5 feet and inches. Your friend s height is 5.6 feet. Who is taller? Eplain. Copyright Big Ideas Learning, LLC Big Ideas Math Blue 155

2 Name Date Chapter 8 Graph the inequality. Fair Game Review (continued) 8. < > > 5 1. The deepest free dive by a human in the ocean is 17 feet. The depth humans have been in the ocean can be represented by the inequality 17. Graph the inequality. 156 Big Ideas Math Blue Copyright Big Ideas Learning, LLC

3 Name Date 8.1 Writing and Graphing Inequalities For use with Activity 8.1 Essential Question How can you use an inequality to describe a real-life statement? 1 ACTIVITY: Writing and Graphing Inequalities Work with a partner. Write an inequality for the statement. Then sketch the graph of all the numbers that make the inequality true. a. Statement: The temperature t in Minot, North Dakota has never been below 36 F. Inequality: Graph: b. Statement: The elevation e in Wisconsin is at most feet above sea level. Inequality: Graph: ACTIVITY: Writing and Graphing Inequalities Work with a partner. Write an inequality for the graph. Then, in words, describe all the values of that make the inequality true. a b Copyright Big Ideas Learning, LLC Big Ideas Math Blue 157

4 Name Date 8.1 Writing and Graphing Inequalities (continued) c d ACTIVITY: Triangle Inequality Work with a partner. Use 8 to 10 pieces of spaghetti. Break one piece of spaghetti into three parts that can be used to form a triangle. Form a triangle and use a centimeter ruler to measure each side. Round the side lengths to the nearest tenth. Record the side lengths in the table. Repeat the process with two other pieces of spaghetti. in L M S cm Side Lengths That Form a Triangle Small Medium Large S + M Repeat the eperiment by breaking pieces of spaghetti into three pieces that do not form a triangle. Record the lengths in a table. Side Lengths That Do Not Form a Triangle Small Medium Large S + M 158 Big Ideas Math Blue Copyright Big Ideas Learning, LLC

5 Name Date 8.1 Writing and Graphing Inequalities (continued) INDUCTIVE REASONING Write a rule that uses an inequality to compare the lengths of three sides of a triangle. Use your rule to decide whether the following triangles are possible. Eplain. a. 5 b. 5 c What Is Your Answer?. IN YOUR OWN WORDS How can you use an inequality to describe a real-life statement? Give two eamples of real-life statements that can be represented by inequalities. Copyright Big Ideas Learning, LLC Big Ideas Math Blue 159

6 Name Date 8.1 Practice For use after Lesson 8.1 Write the word sentence as an inequality. 1. A number p is no greater than 6.. A number n divided by is no less than 1. Tell whether the given value is a solution of the inequality. 3. q + 7 8; q = 10. 1r < 6; r = 5..k ; k = ; 8 < = Graph the inequality on a number line p 8. z > For your birthday, you want to invite some friends to join you at the movies. Movie tickets cost $8. You can spend no more than $35. Write an inequality to represent this situation. Then solve the inequality to find the greatest number of people you can invite. 160 Big Ideas Math Blue Copyright Big Ideas Learning, LLC

7 Name Date 8. Solving Inequalities Using Addition or Subtraction For use with Activity 8. Essential Question How can you use addition or subtraction to solve an inequality? 1 ACTIVITY: Quarterback Passing Efficiency Work with a partner. The National Collegiate Athletic Association (NCAA) uses the following formula to rank the passing efficiency P of quarterbacks. P = 8.Y + 100C + 330T 00N A Y = total length of all completed passes (in Yards) C = Completed passes T = passes resulting in a Touchdown N = intercepted passes A = Attempted passes M = incomplete passes Attempts Completed Intercepted Incomplete Touchdown Not Touchdown Which of the following equations or inequalities are true relationships among the variables? Eplain your reasoning. a. C + N < A b. C + N A c. T < C d. T C e. N < A f. A > T g. A C M h. A = C + N + M Copyright Big Ideas Learning, LLC Big Ideas Math Blue 161

8 Name Date 8. Solving Inequalities Using Addition or Subtraction (continued) ACTIVITY: Quarterback Passing Efficiency Work with a partner. Which of the following quarterbacks has a passing efficiency rating that satisfies the inequality P > 100? Show your work. Player Attempts Completions Yards Touchdowns Interceptions A B C D ACTIVITY: Finding Solutions of Inequalities Work with a partner. Use the passing efficiency formula to create a passing record that makes the inequality true. Then describe the values of P that make the inequality true. a. P < 0 Attempts Completions Yards Touchdowns Interceptions b. P Attempts Completions Yards Touchdowns Interceptions c. 180 < P 50 Attempts Completions Yards Touchdowns Interceptions 16 Big Ideas Math Blue Copyright Big Ideas Learning, LLC

9 Name Date 8. Solving Inequalities Using Addition or Subtraction (continued) d. P Attempts Completions Yards Touchdowns Interceptions e. P 50 > 80 Attempts Completions Yards Touchdowns Interceptions What Is Your Answer?. Write a rule that describes how to solve inequalities like those in Activity 3. Then use your rule to solve each of the inequalities in Activity IN YOUR OWN WORDS How can you use addition or subtraction to solve an inequality? 6. How is solving the inequality + 3 < similar to solving the equation + 3 =? How is it different? Copyright Big Ideas Learning, LLC Big Ideas Math Blue 163

10 Name Date 8. Practice For use after Lesson 8. Solve the inequality. Graph the solution. 1. < p > y z.1 Write and solve an inequality that represents the value of. 5. The perimeter is less than 15 feet. 6. The height is greater than the base. 5 ft + 7. Your goal is to sell at least 50 boes of cookies for your school fundraiser. a. Write an inequality that represents your goal. 9 in. b. You sell 6 boes. Write and solve a new inequality to represent how many boes you need to sell to reach your goal. 16 Big Ideas Math Blue Copyright Big Ideas Learning, LLC

11 Name Date 8.3 Solving Inequalities Using Multiplication or Division For use with Activity 8.3 Essential Question How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Complete the table. Decide which graph represents the solution of the inequality. Write the solution of the inequality. a ? b. > ? > Copyright Big Ideas Learning, LLC Big Ideas Math Blue 165

12 Name Date 8.3 Solving Inequalities Using Multiplication or Division (continued) ACTIVITY: Writing a Rule Work with a partner. Use a table to solve each inequality. a. 3 > 3 b. c. 6 d. 5 < Write a rule that describes how to solve inequalities like those in Activity 1. Then use your rule to solve each of the four inequalities above. 3 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Complete the table. Decide which graph represents the solution of the inequality. Write the solution of the inequality. a ? Big Ideas Math Blue Copyright Big Ideas Learning, LLC

13 Name Date 8.3 Solving Inequalities Using Multiplication or Division (continued) b. < ? < ACTIVITY: Writing a Rule Work with a partner. Use a table to solve each inequality. a. 1 b. 3 < c. > d Write a rule that describes how to solve inequalities like those in Activity 3. Then use your rule to solve each of the four inequalities above. What Is Your Answer? 5. IN YOUR OWN WORDS How can you use multiplication or division to solve an inequality? Copyright Big Ideas Learning, LLC Big Ideas Math Blue 167

14 Name Date 8.3 Practice For use after Lesson 8.3 Solve the inequality. Graph the solution. 1. 5n < t > 60. q p < 6. 9.m 5 r t 8. > q To win a trivia game, you need at least 60 points. Each question is worth points. Write and solve an inequality that represents the number of questions you need to answer correctly to win the game. 168 Big Ideas Math Blue Copyright Big Ideas Learning, LLC

15 Name Date 8. Solving Multi-Step Inequalities For use with Activity 8. Essential Question How can you use an inequality to describe the area and perimeter of a composite figure? 1 ACTIVITY: Areas and Perimeters of Composite Figures Work with a partner. a. For what values of will the area of the shaded region be greater than 1 square units? b. For what values of will the sum of the inner and outer perimeters of the shaded region be greater than 0 units? c. For what values of y will the area of the trapezoid be less than or equal to 10 square units? 3 y d. For what values of y will the perimeter of the trapezoid be less than or equal to 16 units? Copyright Big Ideas Learning, LLC Big Ideas Math Blue 169

16 Name Date 8. Solving Multi-Step Inequalities (continued) e. For what values of w will the area of the shaded region be greater than or equal to 36 square units? w f. For what values of w will the sum of the inner and outer perimeters of the shaded region be greater than 7 units? g. For what values of will the area of the shaded region be less than π square units? h. For what values of will the sum of the inner and outer perimeters of the shaded region be less than π + 0 units? ACTIVITY: Volume and Surface Area of a Composite Solid Work with a partner. a. For what values of will the volume of the solid be greater than or equal to cubic units? 3 b. For what values of will the surface area of the solid be greater than 7 square units? Big Ideas Math Blue Copyright Big Ideas Learning, LLC

17 Name 8. 3 Date Solving Multi-Step Inequalities (continued) ACTIVITY: Planning a Budget Work with a partner. You are building a patio. You want to cover the patio with Spanish tile that costs $5 per square foot. Your budget for the tile is $1700. How wide can you make the patio without going over your budget? Tiles are needed under the plants. No tile is needed under the hot tub. 6 ft 6 ft ft What Is Your Answer?. IN YOUR OWN WORDS How can you use an inequality to describe the area and perimeter of a composite figure? Give an eample. Include a diagram with your eample. Copyright Big Ideas Learning, LLC Big Ideas Math Blue 171

18 Name Date 8. Practice For use after Lesson 8. Solve the inequality. Graph the solution. d > n < z < ( p + 3) > 6. ( y ) 7. In the United States music industry, an album is awarded gold certification with at least 500,000 albums sold. A recording artist is selling about 100 albums each day. The artist has already sold 15,000 albums. About how many more days will it take before the album is awarded gold certification? 17 Big Ideas Math Blue Copyright Big Ideas Learning, LLC

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