1. 3.1 Inequalities and Their Graphs:
Inequality: A mathematical sentence that uses and inequality symbol (< , >, ≤, ≥) to compare the values of two expressions.
Solution of an Inequality: Any number that makes the inequality true.

2. x < -1 SYMBOLS OF INEQUALITY:
( < ) Less than : Any number that is to the left not including the number itself.
x < -1

3. x > 1 SYMBOLS OF INEQUALITY:
( > ) Greater than: Any number that is to the right not including the number itself.
x > 1

4. x ≤ 0 SYMBOLS OF INEQUALITY:
( ≤ ) Less than or equal to : Any number that is to the left including the number itself.
x ≤ 0

5. x ≥ 2 SYMBOLS OF INEQUALITY:
( ≥ ) Greater than or equal to : Any number that is to the right including the number itself.
x ≥ 2

6. GOAL:

7. WRITING INEQUALITIES:
We can use the inequality symbols to write verbal expressions into math sentences and use the number line to represent the solution.
Ex: All real numbers greater than 3.

8. WRITING INEQUALITIES: (SOLUTION)
All real numbers greater than 3.
Let x = real numbers
x > 3
Greater than  >
Graph:

9. REAL-WORLD:
Joseph saved last month a total of $115 dollars for doing house shores. He is planning to spend $30 on a video game and the he wants to buy music sheet booklets. If each booklet costs $15, create a graph to represent the number of booklets he can buy.

10. Solution:
Joseph saved  $115
Buys video game  - 30
Music sheet booklets  $15x
To find how many he can buy:
15x + 30 ≤ 150
Subtract 30
Divide by 15
15x ≤ 120
x ≤ 8 booklets.

11. YOU TRY IT:
Ex: What inequality represent the verbal expression:
The subtraction of t and 7 is less than -3.

12. The sum and t and 7 is less than -3.
SOLUTION:
The sum and t and 7 is less than -3.
t, 7, - 3
subtraction  -
t - 7 < -3
Less than  <
Graph: ( isolate t  t < 4)

13. IDENTIFYING SOLUTIONS:
We can use substitution to see if a given number is a solution to an equation.
Ex: Identify solutions by evaluation: – 7y ≤ 6
a) 1 b) -1, c) 3 d) -5

14. SOLUTION:
13 – 7y ≤ 6
a) – 7( 1) ≤ 6
13 – 7 ≤ 6
6 ≤ 6 TRUE
Thus 1 is a solution.
13 – 7y ≤ 6
a) – 7( -1) ≤ 6
≤ 6
20 ≤ 6 FALSE
Thus -1 is NOT a solution.

15. SOLUTION:
13 – 7y ≤ 6
a) – 7( 3) ≤ 6
13 – 21 ≤ 6
-7 ≤ 6 TRUE
Thus 3 is a solution.
13 – 7y ≤ 6
a) – 7( 5 ) ≤ 6
≤ 6
- 12 ≤ 6 TRUE
Thus 5 is a solution.

16. GRAPHING: Always isolate variables and then graph.
x < -1
x > 1
x ≤ 0
x ≥ 2

17. Graphing Inequalities
VIDEOS:
Graphing Inequalities

18. CLASSWORK: Page
Problems: As many as needed to master the
concept.