This document provides examples and explanations for graphing inequalities on a number line. It begins by defining key inequality terms like true/false inequalities and open inequalities. Examples are then provided to demonstrate how to identify which numbers satisfy given inequalities and how to graph the solutions of inequalities on a number line. The examples illustrate how to write an inequality to describe a real-world scenario and graph its solution. Homework practice problems are assigned at the end.

1. SECTION 3-6
Graphing Inequalities on a Number Line

2. ESSENTIAL QUESTIONS
How do you determine if a number is a solution of an
inequality?
How do you graph the solution of an inequality on a
number line?
Where you’ll see this:
Business, government, sports, physics, geography

3. VOCABULARY
1. Inequality:
2. True Inequality:
3. False Inequality:
4. Open Inequality:
5. Solution of the Inequality:

4. VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality:
3. False Inequality:
4. Open Inequality:
5. Solution of the Inequality:

5. VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisfies the
conditions
3. False Inequality:
4. Open Inequality:
5. Solution of the Inequality:

6. VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisfies the
conditions
3. False Inequality: When the given inequality does not satisfy
the conditions
4. Open Inequality:
5. Solution of the Inequality:

7. VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisfies the
conditions
3. False Inequality: When the given inequality does not satisfy
the conditions
4. Open Inequality: When there is a variable in the inequality
5. Solution of the Inequality:

8. VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
sign in it
2. True Inequality: When the given inequality satisfies the
conditions
3. False Inequality: When the given inequality does not satisfy
the conditions
4. Open Inequality: When there is a variable in the inequality
5. Solution of the Inequality: Find all values that make the
inequality true

9. SYMBOLS

10. SYMBOLS
<, >, ≤, ≥, ≠

11. SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
Less than Maximum Minimum

12. SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥
Less than Maximum Minimum

13. SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤
Less than Maximum Minimum

14. SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum

15. SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum
<

16. SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum
< ≤

17. SYMBOLS
<, >, ≤, ≥, ≠
At least At most Greater than
≥ ≤ >
Less than Maximum Minimum
< ≤ ≥

18. EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2

19. EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2

20. EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2

21. EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2

22. EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
No

23. EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
No Yes

24. EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
is a solution.
A. x ≤ 1 B. x < 1 C. − 2 < x < 2
Yes No Yes
1 1
D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤
2 2
No Yes No

25. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2

26. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6

27. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6

28. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6

29. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6

30. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6

31. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6

32. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6

33. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6

34. EXAMPLE 2
Graph the solution of each inequality on a number line.
a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
-4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6

35. EXAMPLE 3
By order of the fire commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
b. Graph the solution of the inequality on a number line.

36. EXAMPLE 3
By order of the fire commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
b. Graph the solution of the inequality on a number line.

37. EXAMPLE 3
By order of the fire commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.

38. EXAMPLE 3
By order of the fire commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250

39. EXAMPLE 3
By order of the fire commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250

40. EXAMPLE 3
By order of the fire commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250

41. EXAMPLE 3
By order of the fire commissioner, the capacity of a local
theatre is not to exceed 225 people.
a. Write an inequality that describes the capacity of the
theatre.
Let p be the number of people
0 ≤ p ≤ 225
b. Graph the solution of the inequality on a number line.
0 50 100 150 200 250

42. HOMEWORK

43. HOMEWORK
p. 128 #1-43 odd
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