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

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

MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable. NGSSS

Key Concept

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

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

Solve p ≥ 9. Graph the solution set on a number line. 1 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 The solution is p ≥ 18. Graph the solution set. Draw a closed dot at 18 with an arrow to the right. Answer: Example 2

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

Key Concept 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

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 3 CYP

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

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

BOOKS Jesse is filling a box with books that weigh 2 pounds each 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

Division Property of Inequality 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

C. 13x ≤ 5; at most 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. 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 Example 5 CYP

Solve the inequality −3w > −6 Solve the inequality −3w > −6. Graph the solution set on a number line. A. w > 2 B. w < 2 C. w < –2 D. w > –2 Five Minute Check 1

Solve the inequality –j ≤ 7. Graph the solution set on a number line. A. j ≥ –7 B. j ≤ –7 C. j ≥ 7 D. j ≤ 7 Five Minute Check 2

A video game rental store charges $5 per game per month A video game rental store charges $5 per game per month. It also offers a pre-payment card of $50 for an unlimited number of games per month. Write and solve an inequality to find out how many games per month a customer should rent in order to make the pre-payment card less expensive than paying per game per month. Interpret the solution. A. 5g > 50; g < 10; A customer should rent less than 10 games per month. B. > 50; g > 250; A customer should rent more than 250 games per month. C. 5g > 50; g > 10; A customer should rent more than 10 games per month. D. 5g > 50; g < 250; A customer should rent less than 250 games per month _ g 5 Five Minute Check 3