1. Intervals and Inequalities
World 3-3
Intervals and Inequalities

2. Eg 1. Place the following #’s on a number line.
-6, 5 , 251/2, -1 & - 10 -1 3 5 2 -6
- 10
251/2 2 4 6 8 10 -2 -4 -6 -8

3. Sometimes it is useful to talk about a RANGE of numbers.
There are 3 ways to accomplish this.

4. Identifies the interval of numbers The end number IS in the set
1) Number Line 2 4 6 8 10 -2 -4 -6 -8
Identifies the interval of numbers
The end number IS in the set
The end number IS NOT in the set

5. 2) Bracket Notation [ -2, 8 [ Lowest # Highest # -5, 7 [ ] 5, 9 ] [
HUGGING brackets mean the end number it is CONTAINED in the set.
BACK FACING brackets means the end number is NOT CONTAINED in the set.

6. Greater than 10 _________ At Most 22 _________ At Least 15 _________
Eg. 2 Inequalities Language
The mouth always OPENS
to the larger number.
x 5 x
Less than _________
Greater than 10 _________
At Most _________
At Least _________ x x

7. 3) Set Notation
{ x R | x 8 }
x is a real #
Lowest #
Highest #

8. Intervals [a,b] [a,b[ ]a,b] ]a,b[ Closed Left Closed Right Open
Bracket
Set-Builder
Number Line
Closed
Left Closed
Right Open
Left Open
Right Closed
Open
[a,b] b a b a
[a,b[
]a,b] b a b a
]a,b[

9. World 3-3