1. 3.1 Inequalities and their graphs
Today we will write, graph, and identify solutions of inequalites.

2. Inequalities
A statement that one quantity is less than or greater than another.
Symbols
Everyday Phrase
Inequality
Less than
<
Less than or equal to ≤
Greater than
>
Greater than or equal to ≥
g is greater than or equal to 6
g ≥ 6
Below 400
t < 40
fewer than 20 calories
c < 20
At most $10
p ≤ 10
b is less than 4
b < 4

3. 3x – 5 > 20 3x – 5 > 20 3x – 5 > 20 -3 11 -9 – 5 > 20
Solution of an inequality:
--Any number(s) that makes the inequality true.
Determine whether each number is a solution of the given inequality.
3x – 5 > a b c. 11
3x – 5 > 20
3x – 5 > 20
3x – 5 > 20 -3 ? ? ?
3( ) – 5 > 20
3( ) – 5 > 20
3( ) – 5 > 20 11 ? ? ?
-9 – 5 > 20
0 – 5 > 20
33 – 5 > 20 ? ?
-14 > 20 ?
28 > 20
– 5 > 20 no no
yes

4. Graphing Inequalities
Mark your point(s) with the correct dot
Draw a line from the points to show the solution set
t > 3
x ≤ 5
Less than
< ○
Greater than
>
Less than or equal to ≤ ●
Greater than or equal to ≥

5. a. x > -4 b. x < 0 c. 3 < x x > 3
Got It? What is the graph of each inequality?
a. x > -4
b. x < 0
c. 3 < x
x > 3

6. Write an inequality for each graph.x
< x
> x
>

7. Assignment
Book page 168: 8-11, even, 29-36