2. 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

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

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

5. Key Concept

6. 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

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

8. 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

9. 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

10. 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

11. Key Concept 3

12. 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

13. 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

14. 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

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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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 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