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Interval Notation

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**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

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**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

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**-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)

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**Let’s look at it from the answer!**

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**(-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

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**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 ∞

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**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]

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Solving Inequalities We can solve inequalities just like equations, with the following exception: Multiplication or division of an inequality by a negative.

Solving Inequalities We can solve inequalities just like equations, with the following exception: Multiplication or division of an inequality by a negative.

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