1. Interval Notation

2. Interval Notation- Uses inequalities to describe subsets of real numbers.
Example:
This is an example of a Bounded Interval
That is because x is in the middle or bound by the numbers on the end
-2 ≤ x < 6

3. We will use brackets and parenthesis to represent the numbers that x can be
Since x can be equal to -2 we use a bracket: [
This means that x starts at -2 and can be equal to it
-2 ≤ x < 6
[-2

4. -2 ≤ x < 6 [-2 , 6) Since x cannot be 6, we’ll use a parenthesis )
This means that x is less than 6 and cannot equal it
-2 ≤ x < 6
[-2
, 6)

5. Let’s look at it from the answer!

6. (-5, 9] = -5 9 < x ≤ -5 is the starting point on the left
Write an inequality to represent the following interval notation:
(-5, 9]
= -5 9
< x ≤
-5 is the starting point on the left
Parenthesis mean not equal
9 is the end point on the right
Bracket means it is equal to

7. x ≤ 6 ∞ Unbounded Interval
Example: Write the following in interval notation:
In this case the x is not in the middle of two numbers
That means it’s not “bound”
There are a infinite amount of numbers that are less than 6, so we’re going to have to use the infinity sign
x ≤ 6 ∞

8. x ≤ 6 (-∞ , 6] Since x is smaller than 6, the 6 is the right bound
Use a bracket since it can be equal to
The other side has an infinite number of solutions, so we’ll use the infinity sign
Since it goes on forever in a negative direction, ∞ has to be negative
Since you can’t equal infinity, use a parenthesis
(-∞
, 6]