1. Intersection, Unions, and Compound Inequalities

2. Intersection
A collection of items that overlap all parts, or Items that all parts have in common.
Words you could see : AND / INTERSECTION
Symbol you could see : 
How to find given different formats
Graph : The section where the two graphs overlap.
Set of Numbers : The numbers that are in both (all) sets.

3. Notations for Answers Roster Method Graphing Notation
List ALL answers in a set, {}.
Graphing Notation
Uses a graph to show where all the answers are located.
Brackets or filled in circle to include the value.
Parentheses or open circle to not include the value.
Set Builder Notation
Uses inequalities in a set notation, {x | a < x < b}
Interval Notation
smallest value, largest value.
Brackets to include the value.
Parentheses to not include the value.

4. Types of Answers Type of Answer Graphing Notation Set Builder Notation
Interval notation
No Solution
{x | } , no solution
(,) , no solution
One Solution
{x | a ≤ x ≤ a}
[a, a]
Group of Solutions
{x | a ≤ x ≤ b}
Inequalities could change
[a, b]
Brackets could change
Infinite Solutions
{x | -∞ < x < ∞}
(-∞, ∞)

5. Example
Given the sets, find the intersection, and write answer in Roster Method
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10, 12, 14, 16}
A  B :

6. Example
Given the sets, find the intersection, and write answer in Roster Method
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10, 12, 14, 16}
A  B : {2, 4, 6, 8, 10}

7. Example
Given the intervals, find the intersection, and write answer in GN, SBN and IN.
X > 2
X < 8
Graph x

8. Example
Given the intervals, find the intersection, and write answer in GN, SBN and IN.
X > 2
X < -8
Graph x

9. Example
Given the intervals, find the intersection, and write answer in GN, SBN and IN.
X > 2
X ≥ 8
Graph x

10. Union Bringing together all parts as one.
Words you could see : OR / UNION
Symbol you could see : 
How to find given different formats
Graph : The section where you see at least one line.
Set of Numbers : The collection of all numbers.

11. Example
Given the sets, find the union, and write answer in Roster Method
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10, 12, 14, 16}
A  B :

12. Example
Given the sets, find the union, and write answer in Roster Method
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {2, 4, 6, 8, 10, 12, 14, 16}
A  B : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16}

13. Example
Given the intervals, find the union, and write answer in GN, SBN and IN.
X > 2
X < 8
Graph x

14. Example
Given the intervals, find the union, and write answer in GN, SBN and IN.
X > 2
X < -8
Graph x

15. Example
Given the intervals, find the union, and write answer in GN, SBN and IN.
X > 2
X ≥ 8
Graph x

16. Compound Inequalities
Compound Inequalities are more than one inequality.
Solve each problem separately and then, depending on the conjunction (and / or) or symbol, find the corresponding answers.

17. Example
Solve the compound inequalities and write answer in all three methods (SBN, IN and GN)
-6 ≤ t + 1 and t + 8 < 2 t

18. Example
Solve the compound inequalities and write answer in all three methods (SBN, IN and GN)
-4 ≤ 3n + 5 and 2n - 3 ≤ 7 n

19. Example
Solve the compound inequalities and write answer in all three methods (SBN, IN and GN)
x + 5 < -3 or x + 5 ≥ 4 x

20. Example
Solve the compound inequalities and write answer in all three methods (SBN, IN and GN)
5 – 3x < 8 or 2x + 1 > 7 x

21. Example
Solve and write answer in SBN, IN and GN
-1 < 2x – 3 ≤ 6

22. Homework
Section 9.2 # 7-16, 17, 18, 27, 28, 36, 38,
51, 53, 57, 63, 73, and 77