1. Inequalities and their Graphs
Chapter 3 Section 1
Inequalities and their Graphs

2. What do Inequalities Mean?
You already know that equations are mathematical statements that describe two expressions with equal values. When the values of two expressions are not equal, their relationship can be described in an inequality.

3. What do Inequalities Mean?
<
>
Less than
Fewer than
Less than or equal to
At most
No more than
a maximum of
Greater than
More than
Greater than or equal to
At least
No less than
A minimum of

4. Let’s see some examples
Suppose the minimum driving age in your state is 16. Write an inequality to describe people who are of legal driving age in your state.
Let d represent the ages of people who are of legal driving age
Are greater than or equal to
The ages of all drivers
16 years d 16

5. What do Inequality Graphs look like?
<
>
Less than has an open ended graph, and the arrow points to the left
Less than or equal to has a CLOSED ended graph and points to the left
Greater than has an open ended graph and the arrow points to the right
Greater than or equal to has a closed ended graph and points the right

6. Notice…
The “Equals To” graphs are closed, while the less than or greater than is not closed.
Think of it like this, if it has an extra bar in the symbol, it is closed.

7. Let’s look at some graphs
Graph these please.
Hint: remember when you are supposed to use a filled or empty circle.

8. Your turn! Graph these please.
Hint: remember when you are supposed to use a filled or empty circle.

9. One more problem… Find the numbers that make this inequality true. 4-6 -4 1 3 -7 no
yes
yes
Hint: plug it in, plug it in no no
yes

10. Assignment
Page 134
#2-48 evens
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