1. Splash Screen

2. Five-Minute Check (over Lesson 1–5) CCSS Then/Now New Vocabulary
Key Concept: “And” Compound Inequalities
Example 1: Solve an “And” Compound Inequality
Key Concept: “Or” Compound Inequalities
Example 2: Solve an “Or” Compound Inequality
Example 3: Solve Absolute Value Inequalities
Key Concept: Absolute Value Inequalities
Example 4: Solve a Multi-Step Absolute Value Inequality
Example 5: Real-World Example: Write and Solve an Absolute Value Inequality
Lesson Menu

3. Solve the inequality 3x + 7 > 22
Solve the inequality 3x + 7 > 22. Graph the solution set on a number line.
A. {x | x > 5}
B. {x | x < 5}
C. {x | x > 6}
D. {x | x < 6}
5-Minute Check 1

4. Solve the inequality 3(3w + 1) ≥ 4. 8
Solve the inequality 3(3w + 1) ≥ 4.8. Graph the solution set on a number line.
A. {w | w ≤ 0.2}
B. {w | w ≥ 0.2}
C. {w | w ≥ 0.6}
D. {w | w ≤ 0.6}
5-Minute Check 2

5. Solve the inequality 7 + 3y > 4(y + 2)
Solve the inequality 7 + 3y > 4(y + 2). Graph the solution set on a number line.
A. {y | y > 1}
B. {y | y < 1}
C. {y | y > –1}
D. {y | y < –1}
5-Minute Check 3

6. Solve the inequality . Graph the solution set on a number line.
A. {w | w ≤ –9}
B. {w | w ≥ –9}
C. {w | w ≤ –3}
D. {w | w ≥ –3}
5-Minute Check 4

7. Mathematical Practices 5 Use appropriate tools strategically.
CCSS

8. You solved one-step and multi-step inequalities.
Solve compound inequalities.
Solve absolute value inequalities.
Then/Now

9. compound inequality
intersection
union
Vocabulary

10. Concept

11. Solve 10  3y – 2 < 19. Graph the solution set on a number line.
Solve an “And” Compound Inequality
Solve 10  3y – 2 < 19. Graph the solution set on a number line.
Method 1 Solve separately.
Write the compound inequality using the word and. Then solve each inequality.
10  3y – 2 and 3y – 2 < 19
12  3y 3y < 21
4  y y < 7
4  y < 7
Example 1

12. Method 2 Solve both together.
Solve an “And” Compound Inequality
Method 2 Solve both together.
Solve both parts at the same time by adding 2 to each part. Then divide each part by 3.
10  3y – 2 < 19
12  3y < 21
4  y < 7
Example 1

13. Answer: The solution set is y | 4  y < 7.
Solve an “And” Compound Inequality
Graph the solution set for each inequality and find their intersection.
4  y < 7
y < 7
y  4
Answer: The solution set is y | 4  y < 7.
Example 1

14. What is the solution to 11  2x + 5 < 17?B. C. D.
Example 1

15. Concept

16. Solve each inequality separately. –x  –4 or x + 3 < 2 x < –1
Solve an “Or” Compound Inequality
Solve x + 3 < 2 or –x  –4. Graph the solution set on a number line.
Solve each inequality separately.
–x  –4 or
x + 3 < 2
x < –1
x  4
x < –1 or x  4
x < –1
x  4
Answer: The solution set is x | x < –1 or x  4.
Example 2

17. What is the solution to x + 5 < 1 or –2x  –6
What is the solution to x + 5 < 1 or –2x  –6? Graph the solution set on a number line. A. B. C. D.
Example 2

18. A. Solve 2 > |d|. Graph the solution set on a number line.
Solve Absolute Value Inequalities
A. Solve 2 > |d|. Graph the solution set on a number line.
2 > |d| means that the distance between d and 0 on a number line is less than 2 units. To make 2 > |d| true, you must substitute numbers for d that are fewer than 2 units from 0.
Notice that the graph of 2 > |d| is the same as the graph of d > –2 and d < 2.
All of the numbers between –2 and 2 are less than 2 units from 0.
Answer: The solution set is d | –2 < d < 2.
Example 3

19. B. Solve 3 < |d|. Graph the solution set on a number line.
Solve Absolute Value Inequalities
B. Solve 3 < |d|. Graph the solution set on a number line.
3 < |d| means that the distance between d and 0 on a number line is greater than 3 units. To make 3 < |d| true, you must substitute values for d that are greater than 3 units from 0.
Notice that the graph of 3 < |d| is the same as the graph of d < –3 or d > 3.
All of the numbers not between –3 and 3 are greater than 3 units from 0.
Answer: The solution set is d | d < –3 or d > 3.
Example 3

20. A. What is the solution to |x| > 5?B. C. D.
Example 3a

21. B. What is the solution to |x| < 5?
A. {x | x > 5 or x < –5}
B. {x | –5 < x < 5}
C. {x | x < 5}
D. {x | x > –5}
Example 3b

22. Concept

23. Solve |2x – 2|  4. Graph the solution set on a number line.
Solve a Multi-Step Absolute Value Inequality
Solve |2x – 2|  4. Graph the solution set on a number line.
|2x – 2|  4 is equivalent to 2x – 2  4 or 2x – 2  –4.
Solve each inequality.
2x – 2  4 or 2x – 2  –4
2x  6 2x  –2
x  3 x  –1
Answer: The solution set is x | x  –1 or x  3.
Example 4

24. What is the solution to |3x – 3| > 9
What is the solution to |3x – 3| > 9? Graph the solution set on a number line. A. B. C. D.
Example 4

25. End of the Lesson

26. Pages 45 – 47
#12 – 16, 23, 28, 33,34, 37, 45, 50, 53