Lesson Menu Main Idea Key Concept:Properties of Inequality Example 1:Solve Inequalities Example 2:Solve Inequalities Key Concept:Properties of Inequality Example 3:Multiply by a Negative Number Example 4:Divide by a Negative Number Example 5:Real-World Example

Main Idea/Vocabulary Solve and graph one-step inequalities by using the Multiplication or Division Properties of Inequality.

Key Concept

Example 1 Solve Inequalities Solve 6x < –30. Graph the solution set on a number line. 6x <–30Write the inequality. x <– 5Simplify. Draw an open dot at –5 with an arrow to the left. Division Property of Inequality Answer:

Example 1 CYP Solve 21 < 3n. Graph the solution set on a number line. A.n < 7 B.n > 7 C.n < –7 D.n > –7

Example 2 Solve Inequalities Solve p ≥ 9. Graph the solution set on a number line. __ 1 2 Write the inequality. Multiplication Property of Inequality Simplify.

Example 2 The solution is p ≥ 18. Graph the solution set. Solve Inequalities Answer: Draw a closed dot at 18 with an arrow to the right.

Example 2 CYP Solve  –2. Graph the solution set on a number line. __ k 6 A.k ≤ 12 B.k ≤ –12 C.k ≥ 12 D.k ≥ –12

Key Concept 3

Example 3 Multiply or Divide by a Negative Number Solve the inequality ≤ 5. Graph the solution set on a number line. __ b –4 Write the inequality. Multiplication Property of Inequality; reverse inequality symbol Simplify. Answer:

Example 3 CYP Solve > –3. Graph the solution set on a number line. __ h –6 A.h < 18 B.h > 18 C.h < –18 D.h > –18

Example 4 Solve the inequality –4n > –60. Graph the solution set on a number line. Multiply or Divide by a Negative Number Write the inequality. Division Property of Inequality; reverse inequality symbol Simplify. Answer:

Example 4 CYP Solve –8n  72. Graph the solution set on a number line. A.n ≤ –9 B.n ≥ –9 C.n ≤ 9 D.n ≥ 9

Example 5 BOOKS Jesse is filling a box with books that weigh 2 pounds each. The box can hold at most 15 pounds of books. Assuming that space is not an issue, write and solve an inequality to find how many books Jesse can put in the box. The phrase at most means less than or equal to. Let p = the number of books in the box.

Example 5 Write the inequality. Division Property of Inequality Simplify. Answer:The solution is p ≤ 7.5. He can put at most 7 books in the box.

Example 5 CYP A.5x ≤ 13; at most 2.6 pounds B.5x ≥ 13; at least 2.6 pounds C.13x ≤ 5; at most about 0.4 pound D.13x ≥ 5; at least about 0.4 pound MONEY Victor has $13 to buy trail mix for a hiking trip. A pound of trail mix costs $5. Write and solve an inequality to find how many pounds of trail mix Victor can buy.