Solving Two-Step Inequalities COURSE 3 LESSON 2-8 Solve –5x – 2 > –12. –5x – 2 > –12 –5x – 2 + 2 > –12 + 2 Add 2 to each side. –5x > –10 Simplify. Divide each side by –5. Reverse the direction of the inequality. –10 –5 –5x < x < 2 Simplify. 2-8

Solving Two-Step Inequalities COURSE 3 LESSON 2-8 (continued) Check Step 1 See if 2 is a solution to the related equation. –5x – 2 = –12 Write the related equation. –12 = –12 –5(2) – 2 = –12 Substitute 2 for x. –10 – 2 = –12 Use the order of operations. Step 2 Check the inequality symbol. Choose any number less than 2 and substitute it into the original inequality. In this case, try 0. –5x – 2 > –12 –5(0) – 2 > –12 Substitute 0 for x. –2 > –12 2-8

Solving Two-Step Inequalities COURSE 3 LESSON 2-8 You have $50 to spend on CDs that cost $7 each and one CD player that costs $29. How many CDs can you buy? cost of one CD player < – Words plus cost of CDs is at most $50 Let c = the number of CDs. Inequality 29 + 7 • c 50 29 + 7 • c 50 < – 2-8

Solving Two-Step Inequalities COURSE 3 LESSON 2-8 (continued) 29 – 29 + 7 • c 50 – 29 Subtract 29 from each side. < – 7c 21 Simplify. < – Divide each side by 7. < – 7c 7 21 c 3 Simplify. You can buy 3 CDs. Check for Reasonableness Each CD costs $7. The cost of the CD player plus three CDs would be $7(3) + $29, or $50, the amount you have to spend. You would spend $50 or less if you bought the CD player and 3 or fewer CDs. 2-8

Solving Two-Step Inequalities COURSE 3 LESSON 2-8 Solve. 1. 3x – 11 > 10 2. + 5 –2 3. You want to order one large photo of yourself for $8.95 and some small photos for your friends. The small photos cost $.75 each. You have $25 to spend. Write an inequality you can use to find how many small photos you can order. Then solve it. r –4 > – x > 7 r 28 < – 0.75p + 8.95 25; p 21.4; 21 or fewer small photos < – 2-8