This document discusses inequalities and their graphs. It defines an inequality as a statement that two expressions are not equal. It explains the symbols used in inequalities like <, >, ≤, and ≥ and how to graph them correctly, with open or closed circles depending on if it's a < or ≤. Examples are provided of writing and graphing simple one-variable inequalities and having the reader practice graphing some on their own. Key points covered include understanding the direction the solution goes based on if the variable is on the left side of the inequality sign.

1. Inequalities and their Graphs
x>5 x>5
2 3 4 5 6 7 8

2. Inequalities and their
Graphs
Objective: To write and
graph simple inequalities with
one variable

3. Inequalities and their Graphs
What is a good definition
for Inequality?
An inequality is a statement that
two expressions are not equal
2 3 4 5 6 7 8

4. Inequalities and their Graphs
Terms you see and need to know
to graph inequalities correctly
< less than Notice
open
> greater than circles

5. Inequalities and their Graphs
Terms you see and need to know
to graph inequalities correctly
≤ less than or equal to
≥ greater than or equal to
Notice colored in circles

6. Inequalities and their Graphs
Let’s work a few together
Notice: when variable is
on left side, sign shows
x >3 direction of solution
3

7. Inequalities and their Graphs
Let’s work a few together
Notice: when variable is
x<7
on left side, sign shows
direction of solution
7

8. Inequalities and their Graphs
Let’s work a few together
Notice: when variable is
p ≤ −2 on left side, sign shows
direction of solution
-2 Color in
circle

9. Inequalities and their Graphs
Let’s work a few together
Notice: when variable is
x≥8
on left side, sign shows
direction of solution
8
Color in circle

10. Try this one on your own
x > 12

11. 12

12. On your Own
s < 12

13. 12

14. On your Own
m≥2

15. 2

16. Answer 1 through 5
b ≤ −6
1.

17. On your Own
x > 10
2.

18. On your Own
p > − 15
3.

19. On your Own
g ≥ 25
4.

20. On your Own
x < 13
5.

21. Answers: 1 through 5
1. 2.
-6 10
3. 4.
-15 25
5.
13

22. Answer 6 through 10
b ≤ -7
6.

23. On your Own
a>8
7.

24. On your Own
q ≥ -5
8.

25. On your Own
s < 14
9.

26. On your Own
m≥8
10.

27. Answers: 6 through 10
6. 7.
-7 8
8. 9.
-5 14
10.
8

28. Graphing
Inequalities
Excellent Job !!! Well Done