1. Day 2 - Interval Notation and Inequalities
Worksheet Key
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

2. Day 2 - Interval Notation and Inequalities
Worksheet Key
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

3. ©2014, viet.dang@humble.k12.tx.us
Inequalities and Interval Notation
©2014,
11/20/2018 2:56 AM11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

4. Day 2 - Interval Notation and Inequalities
Review
Determine the domain and range in Inequality Form
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

5. Labeling Interval Notation on a Coordinate Plane
>, <, or ≠ requires the dot being OPEN
>, <, or = required the dot being CLOSED hole
Written as: Smaller number, bigger number
Brackets [ ] : DO include endpoints INCLUSIVE (think of straight line = line needed for inequality)
Parentheses ( ) : DO NOT include endpoints NOT INCLUSIVE deals with infinity (think of no line = curve)
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

6. Day 2 - Interval Notation and Inequalities
Example 1
Determine the domain and range in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

7. Day 2 - Interval Notation and Inequalities
Example 2
Determine the domain and range in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

8. Day 2 - Interval Notation and Inequalities
Your Turn
Determine the domain and range in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

9. Day 2 - Interval Notation and Inequalities
Example 3
Determine the domain and range in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

10. Day 2 - Interval Notation and Inequalities
Example 4
Determine the domain and range in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

11. Day 2 - Interval Notation and Inequalities
Your Turn
Determine the domain and range in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

12. Graphing Interval Notation On a Number Line
Interval notations involve the symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval
Brackets [ ] : DO include endpoints INCLUSIVE (think of straight line = line needed for inequality)
Parentheses ( ) : DO NOT include endpoints NOT INCLUSIVE deals with infinity (think of no line = curve)
Written as: Smaller number, bigger number
Infinity always deals with parenthesis
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

13. Day 2 - Interval Notation and Inequalities
Example 5
Write the set x > 5 in Interval Notation and graph it on a number line
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

14. Day 2 - Interval Notation and Inequalities
Example 6
Write the set x < 4 in Interval Notation and graph it on a number line
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

15. Day 2 - Interval Notation and Inequalities
Example 7
Write the set –2 < x < 5 in Interval Notation and graph it on a number line
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

16. Day 2 - Interval Notation and Inequalities
Your Turn
Write the set x > 0 in Interval Notation and graph it on a number line
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

17. Day 2 - Interval Notation and Inequalities
Example 8
Express the interval (–∞, 10) as an inequality using the variable x.
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

18. Day 2 - Interval Notation and Inequalities
Your Turn
Express the interval [10, ∞) as an inequality using the variable x.
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

19. Day 2 - Interval Notation and Inequalities
Steps
Isolate the x where the variable in on the left side
Solve as if it was EQUAL to 0. These values are called critical values.
FOLLOW THE ARROW
Plot the critical values on a number line and graph. Please always label zero.
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

20. Day 2 - Interval Notation and Inequalities
Example 9
Solve x – 4 < –3, write the answer in Inequality form and graph on a number line
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

21. Day 2 - Interval Notation and Inequalities
Example 10
Solve 5x – 6 < 4x – 4, write the answer in Inequality form and graph on a number line
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

22. Day 2 - Interval Notation and Inequalities
Your Turn
Solve 5x + 3 > 4x + 5, write the answer in Interval Notation and graph on a number line
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

23. Day 2 - Interval Notation and Inequalities
Rule
When we negative divide, we must flip the sign.
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

24. Example 11
Solve –3/4x > 18, write the answer in Interval Notation, and graph on a number line
When we negative divide, we flip the sign
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

25. Example 12
Solve –5(x – 1) < 10, write the answer in Interval Notation and graph on a number line
When we negative divide, we flip the sign
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

26. Day 2 - Interval Notation and Inequalities
Example 13
Solve 4(x – 3) > 9(x + 1), write the answer in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

27. Day 2 - Interval Notation and Inequalities
Your Turn
Solve 3(x + 1) < 5(x – 2), write the answer in Interval Notation
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities

28. Day 2 - Interval Notation and Inequalities
Assignment
Worksheet 2
11/20/2018 2:56 AM
Day 2 - Interval Notation and Inequalities