1. Inequalities

2. Symbols:
< less than
> Greater than
≤ less than or equal to
≥ greater than or equal to
Example:
X > 4
Solution of an inequality is a value of the variable that makes the inequality true. An inequality has MORE THAN ONE solution.

3. When we have an inequality we represent it 2 different ways:
1). An inequality statement
x ≤ 6
2). A picture Always use an arrow at the end!

4. How to make an inequality a picture
First: If you have the symbol greater than or less than you an OPEN CIRCLE
If you have the symbol greater than or equal to or less than or equal to you use a closed circle
Practice: 1). X > -7 2). F ≥ -2 3). -6 < h

5. Solving inequalities Same rules and steps as solving equations
ONE EXCEPTION THOUGH:
When you multiply or divide BOTH SIDES by a negative number you must flip the inequality sign
Why?
-3x > 9

6. Solve the inequalities and graph the solution.
1). 3x > -12
2). 2x – 6 < 9
3) ≤ 2(2x -4)
4). -6x – 3 > -4(x +1)

7. Think about what numbers can be a solution for this statement:
-6 < x < 10

8. Compound inequalities
There is more than one solution, but the solutions are in between two real numbers
Graphing compound solutions -6 < x < 10

9. Solving Compound Inequalities
We must perform the same operation to ALL 3 PARTS
-6 < 2x + 4 < 12
-10 < 2x < 8
-5 < x < 4
Now graph the compound inequality

10. Interval Notation for Compound Inequalities
-5 < x < 4
No infinity symbols
(-5, 4)
In order from least to greatest.
Examples: Solve the compound inequalities, graph the solution, and write the interval notation
1) ≤ 3x < 9
2). 4 < 3x – 8 < 24
3). -4< 2(x-3) ≤ 4

11. ∞ positive infinity -∞ negative infinity
The third way we represent inequalities is interval notation
If your arrow is going to the right you use positive infinity
If your arrow is going to the left you use negative infinity
If you have ≥ or ≤ then your number will have a bracket
If you have > or < then your number will have a parentheses
∞ positive infinity
-∞ negative infinity
Infinity always has parentheses!!!
Practice:
1). X > -7
2). F ≥ -2
3) < h