Chapter 3Chapter 3Section 1Section 1

Inequalities and their Inequalities and their GraphsGraphs

What do Inequalities Mean?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.

What do Inequalities Mean?What do Inequalities Mean?• Inequalities

< >• 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

Let’s see some examplesLet’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

The ages of all driversAre greater than or equal to 16 years

d 16

What do Inequality Graphs What do Inequality Graphs look like?look like?

• Inequality graphs

< >• 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

Notice…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.

Let’s look at some graphsLet’s look at some graphs• Graph these please.

x 3

x 2

Hint: remember when you are supposed to use a filled or empty circle.

Your turn!Your turn!• Graph these please.

x 0

x 3

Hint: remember when you are supposed to use a filled or empty circle.

One more problem…One more problem…• Find the numbers that make this

inequality true.• 4• -6• -4• 1• 3• -7

3 4x 15

Hint: plug it in, plug it in

no

yes

yes

no

no

yes

AssignmentAssignment• Page 134

– #2-48 evens– # 71