7.7 Solving Inequalities Using Multiplication or Division For use with Activity 7.7 Essential Question How can you use multiplication or division to solve an inequality? 2 1 ACTIVITY: Writing an Inequality Work with a partner. A store has a clearance rack of shirts that each cost * the same amount. You buy 2 shirts and have money left after paying with a $20 bill. a. Which of the following represents your purchase? What does x represent? Explain your reasoning. 2x < 20 2x > 20 b. Graph the possible values of x on a number line. Explain how you decided what to graph. 2x 20 c. Can you buy a third shirt? Explain your reasoning. 114 2x 2 20 ACTIVITY: Writing an Inequality Work with a partner. One of your favorite stores is having a 75% off sale. You have $20. You want to buy a pair of jeans. a. Which of the following represents your ability to buy the jeans with $20? What does x represent? Explain your reasoning. x < 20 -x > 20 4 -xs 20 4 -x220 7.7 3 Solving Inequalities Using Multiplication or Division (continued) b. Graph the possible values of x on a number line. Explain how you decided what to graph. c. Can you afford a pair of jeans that originally costs $100? Explain your reasoning. ACTIVITY: Solving Inequalities Work with a partner. Complete the following steps for Activity 1. Then repeat the steps for Activity 2. . Use your inequality from part (a). Replace the inequality symbol with an equal sign. Solve the equation. Replace the equal sign with the original inequality symbol. Graph this new inequality. Compare the graph with your graph in part (b). What do you notice? ACTIVITY: Matching Inequalities Work with a partner. Match the inequality with its graph. a. 3x < 9 b. 3x 9 d. 6 < 2x A. B. ++ C. A -8 D. ++ F. -8 -8 E. ++ -8 -8 -6 -6 -6 -4 -4 -4 e. 12 4x -2 -2 -2 -2 0 0 0 0 + 2 2 2 2 2 2 4 4 4 4 C. c. 21 f. 6 6 6 XIN 2 6 < 2 8 8 8 8 8 What Is Your Answer? 5. IN YOUR OWN WORDS How can you use multiplication or division to solve an inequality? Name Practice 7.7 For use after Lesson 7.7 Solve the inequality. Graph the solution. 1. 12q2 36 2. > 6 Graph the numbers that are solutions to both inequalities. 3. 6a 42 and a + 4 > 7 Big Ideas Math Advanced 1 4. d-82 and 9d < 81 5. Each table in a banquet room seats 8 people. The room can seat no more than 360 people. Write and solve an inequality to represent the number of tables in the banquet room.