ACTIVITY: Quarterback Passing Efficiency
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1 3. Solving Inequalities Using Addition or Subtraction solve an inequality? How can you use addition or subtraction to 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. 8.4Y + 100C + 330T 00N P = 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? Explain 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 COMMON CORE Solving Inequalities In this lesson, you will write and solve inequalities using addition or subtraction. solve real-life problems. Learning Standards A.CED.1 A.CED.3 A.REI.3 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 A B C D Chapter 3 Solving Linear Inequalities
2 3 ACTIVITY: Finding Solutions of Inequalities Math Practice Find General Methods What method did you use to choose the values for the formula? Why? 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 b. P c. 180 < P 50 d. P e. P 50 > 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 x + 3 < 4 similar to solving the equation x + 3 = 4? How is it different? Use what you learned about solving inequalities using addition or subtraction to complete Exercises 3 5 on page 114. Section 3. Solving Inequalities Using Addition or Subtraction 111
3 3. Lesson Lesson Tutorials Study Tip You can solve inequalities the same way you solve equations. Use inverse operations to get the variable by itself. Addition Property of Inequality Words If you add the same number to each side of an inequality, the inequality remains true. Numbers 3 < Algebra x 3 > < 6 x > 7 Subtraction Property of Inequality Words If you subtract the same number from each side of an inequality, the inequality remains true. Numbers 3 < 1 Algebra x + 7 > < 4 x > 7 These properties are also true for and. EXAMPLE 1 Solving an Inequality Using Addition Solve x Graph the solution. x 6 10 Write the inequality. Study Tip Undo the subtraction. To check a solution, you check some numbers that are solutions and some that are not Add 6 to each side. x 4 Simplify. The solution is x 4. x Check: x = 5 is not a solution. Check: x = 0 is a solution. Solve the inequality. Graph the solution. 1. b > 9. m > y Chapter 3 Solving Linear Inequalities
4 EXAMPLE Solving an Inequality Using Subtraction Solve 8 > x. Graph the solution. 8 > x Write the inequality. Reading Undo the addition. The inequality 9.4 > x is the same as x < Subtract 1.4 from each side. 9.4 > x Simplify. The solution is x < 9.4. x < Exercises 6 17 Solve the inequality. Graph the solution. 4. k z p >.3 EXAMPLE 3 Real-Life Application On a train, carry-on bags can weigh no more than 50 pounds. Your bag weighs 4.8 pounds. Write and solve an inequality that represents the amount of weight you can add to your bag. Words Variable Weight of your bag plus amount of weight you can add is no more than Let w be the possible weight you can add. the weight limit. Inequality w w 50 Write the inequality Subtract 4.8 from each side. w 5. Simplify. You can add no more than 5. pounds to your bag. 7. WHAT IF? Your carry-on bag weighs 3.5 pounds. Write and solve an inequality that represents the possible weight you can add to your bag. Section 3. Solving Inequalities Using Addition or Subtraction 113
5 3. Exercises Help with Homework 1. REASONING Is the inequality r 5 8 the same as 8 r 5? Explain.. WHICH ONE DOESN T BELONG? Which inequality does not belong with the other three? Explain your reasoning. c c c + 7 c (-6)=3 3+(-3)= 4+(-9)= 9+(-1)= Use the formula in Activity 1 to create a passing record that makes the inequality true. 3. P P + 40 < P 0 1 Solve the inequality. Graph the solution. 6. y t 8 > 4 8. n a + 7 > < v > d g m k h 1.7 < > s + π u ERROR ANALYSIS Describe and correct the error in graphing the solution of the inequality. 8 5 x 5 10 x PROBLEM SOLVING The maximum volume of a great white pelican s bill is about 700 cubic inches. a. A pelican scoops up 100 cubic inches of water. Write and solve an inequality that represents the additional volume the pelican s bill can contain. b. A pelican s stomach can contain about one-third the maximum amount that its bill can contain. Write an inequality that represents the volume of the pelican s stomach. 114 Chapter 3 Solving Linear Inequalities
6 Write and solve an inequality that represents the value of x. 0. The perimeter is less 1. The base is greater. The perimeter is less than 16 feet. than the height. than or equal to 5 feet. 10 in. 10 in. 4 ft x 4 ft 10 m x + 1 in. x 1 in. TIME LEFT: 1 min. 3. REASONING The solution of w + c 8 is w 3. What is the value of c? 4. FENCE The hole for a fence post is feet deep. The top of the fence post needs to be at least 4 feet above the ground. Write and solve an inequality that represents the required length of the fence post. CURRENT SCORE: VIDEO GAME You need at least 1,000 points to advance to the next level of a video game. a. Write and solve an inequality that represents the number of points you need to advance. b. You find a treasure chest that increases your score by 60%. Explain how this changes the inequality. 6. MODELING A circuit overloads at 1800 watts of electricity. A microwave that uses 1100 watts of electricity is plugged into the circuit. Appliance Watts a. Use a model to write and solve an inequality that Clock radio 50 represents the additional number of watts you can Blender 300 plug in without overloading the circuit. Hot plate 100 b. In addition to the microwave, what two appliances in the table can you plug in without overloading the circuit? Toaster 800 Explain. h mm 7. The maximum surface area of the solid is 15π square millimeters. Write and solve an inequality that represents the height of the cylinder. Solve the equation. (Section 1.1) 8. 6 = 3x 9. r 5 = 30. 4c = = 3 b Find the square root. (Skills Review Handbook) Section 3. Solving Inequalities Using Addition or Subtraction 115
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