How can you use multiplication or division to solve an inequality? ACTIVITY: Using a Table to Solve an Inequality
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1 . Solving Inequalities Using Multiplication or Division How can you use multiplication or division to solve an inequality? 1 ACTIVITY: Using a Table to Solve an Inequality Work with a partner. Copy and complete the table. Decide which graph represents the solution of the inequality. Write the solution of the inequality. a ? b. > >? COMMON CORE Solving Inequalities In this lesson, you will solve inequalities using multiplication or division. solve real-life problems. Learning Standards A.CED.1 A.CED. A.REI ACTIVITY: Writing a Rule Work with a partner. Use a table to solve each inequality. a. > b. c. 6 d. 5 < 10 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. 116 Chapter Solving Linear Inequalities
2 ACTIVITY: Using a Table to Solve an Inequality Math Practice Look for Patterns How do the patterns help you complete this activity? Work with a partner. Copy and complete the table. Decide which graph represents the solution of the inequality. Write the solution of the inequality. a ? b. < <? ACTIVITY: Writing a Rule Work with a partner. Use a table to solve each inequality. a. 1 b. < c. > d Write a rule that describes how to solve inequalities like those in Activity. Then use your rule to solve each of the four inequalities above. 5. IN YOUR OWN WORDS How can you use multiplication or division to solve an inequality? Use what you learned about solving inequalities using multiplication or division to complete Eercises 9 on page 11. Section. Solving Inequalities Using Multiplication or Division 117
3 . Lesson Lesson Tutorials Remember Multiplication and division are inverse operations. Multiplication and Division Properties of Inequality (Case 1) Words If you multiply or divide each side of an inequality by the same positive number, the inequality remains true. Numbers 6 < 8 6 > 8 ( 6) < 8 1 < 16 6 > 8 > Algebra < 9 > 1 < ( 9) > 1 < 18 > These properties are also true for and. EXAMPLE 1 Solving an Inequality Using Multiplication Solve > 5. Graph the solution. 8 Undo the division. > 5 Write the inequality > 8 ( 5) Multiply each side by 8. > 0 Simplify. The solution is > 0. > Check: = 80 is not a solution. Check: = 0 is a solution. 1. a <. n w Chapter Solving Linear Inequalities
4 EXAMPLE Solving an Inequality Using Division Solve. Graph the solution. Undo the multiplication. 8 The solution is 8. Write the inequality. Divide each side by. Simplify Check: = 10 is a solution. Check: = 0 is not a solution. Eercises b 6 5. k > > 1.5q Common Error A negative sign in an inequality does not necessarily mean you must reverse the inequality symbol. Only reverse the inequality symbol when you multiply or divide both sides by a negative number. Multiplication and Division Properties of Inequality (Case ) Words If you multiply or divide each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed for the inequality to remain true. Numbers 6 < 8 6 > 8 Algebra ( ) ( 6) > ( ) 8 6 < 8 1 > 16 < < 5 > > < 0 5 > 18 < 6 These properties are also true for and. Section. Solving Inequalities Using Multiplication or Division 119
5 EXAMPLE Solving an Inequality Using Multiplication y Solve >. Graph the solution. y > Write the inequality. Undo the division. y < y < 6 The solution is y < 6. y < 6 Multiply each side by. Reverse the inequality symbol. Simplify Check: y = 9 is a solution. Check: y = 0 is not a solution. EXAMPLE Solving an Inequality Using Division Solve 7y 5. Graph the solution. Undo the multiplication. 7y 5 7y y 5 Write the inequality. Divide each side by 7. Reverse the inequality symbol. Simplify. The solution is y 5. y Check: y = 0 is not a solution. Check: y = 6 is a solution. Eercises p < z 10. 9m > r 1. 0.y 1 10 Chapter Solving Linear Inequalities
6 . Eercises Help with Homework 1. VOCABULARY Eplain how to solve 6 < 5.. WRITING Eplain how solving < 8 is different from solving < 8.. OPEN-ENDED Write an inequality that is solved using the Division Property of Inequality where the inequality symbol needs to be reversed. 9+(-6)= +(-)= +(-9)= 9+(-1)= Use a table to solve the inequality.. < > > n > c m < > 1. w <.5k 17..6y > b. 19. ERROR ANALYSIS Describe and correct the error in solving the inequality. Write the word sentence as an inequality. Then solve the inequality. 0. The quotient of a number and is at most. 1. A number divided by 8 is less than.. Four times a number is at least 1.. The product of 5 and a number is greater than 0. < 5 > ( 5) > 10. CAMERA You earn $9.50 per hour at your summer job. Write and solve an inequality that represents the number of hours you need to work in order to buy a digital camera that costs $7. Section. Solving Inequalities Using Multiplication or Division 11
7 5. COPIES You have $.65 to make copies. Write and solve an inequality that represents the number of copies you can make. 6. SPEED LIMIT The maimum speed limit for a school bus is 55 miles per hour. Write and solve an inequality that represents the number of hours it takes to travel 165 miles in a school bus. 7. n w > 0 9. h < 1 1. y < 11. 7d 56.. > m 5. k > b ERROR ANALYSIS Describe and correct the error in solving the inequality. 7. CRITICAL THINKING Are all numbers greater than zero solutions of > 0? Eplain. m 16 m 16 m 8. TRUCKING In many states, the maimum height (including freight) of a vehicle is 1.5 feet. a. Five crates are stacked vertically on the bed of the truck. Is this legal? Eplain. b. Write and solve an inequality to justify your answer to part (a). 8 in..5 ft Not drawn to scale Write and solve an inequality that represents the value of. 9. Area 10 cm 0. Area < 0 ft 1 cm 10 ft 1 Chapter Solving Linear Inequalities
8 1. TRIP You and three friends are planning a trip. You want to keep the cost below $80 per person. Write and solve an inequality that represents the total cost of the trip.. PRECISION Eplain why the direction of the inequality symbol must be reversed when multiplying or dividing by the same negative number.. PROJECT Choose two musical artists to research. a. Use the Internet or a magazine to complete the table. b. Find and compare the average number of copies sold per month for each CD. Which CD do you consider to be the most successful? Eplain. c. Assume each CD continues to sell at the average rate. Write and solve an inequality that represents the number of months it will take for the total number of copies sold to eceed twice the current number sold. Artist Name of CD Release Date Current Number of Copies Sold 1.. Describe all numbers that satisfy both inequalities. Include a graph with your description.. m > 1 and m < 1 5. n and n 1 6. and 7. m > 5 and m < 10 Solve the equation. (Section 1.) 8. w + 5 = ( ) = v 6 7 = 51. m + 00 = MULTIPLE CHOICE Which of the following is not a solution of p.9 0.8? (Section.) A p =.5 B p =.7 C p =.75 D p = 5 Section. Solving Inequalities Using Multiplication or Division 1
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