1. Objectives:
Graph (and write) inequalities on a number line.
Solve and graph one-variable inequalities. (Linear)
Solve and graph compound inequalities. (Linear)
Solve and graph ABSOLUTE VALUE inequalities.

2. I. Types of Inequalities
1. Greater Than (>): Not Included
2. Less Than (<): Not Included
3. Greater than or equal to (): Included
4. Less Than or Equal To () :Included
5. Equal To (=): Included
6. Not Equal To (): Not Included
SPECIAL NOTES:
If a value is Not Included, this is illustrated with a circle that is not filled in (open circle).
2. If a value is Included, this is illustrated with a circle that is filled in (closed circle).

3. II. Graphing Inequalities
Example 1: x > ½
Test Value:
0 > ½
FALSE
TRUE
Test Value:
1 > ½ -½
Example 2: x  -5
Test Value:
-6  -5
TRUE
FALSE -5 5
Test Value:
0  -5
Example 3: -4 < x
Test Value:
-4 < -5
FALSE
TRUE
Test Value:
-4 < 0 -4 4

4. II. Graphing Inequalities
Example 4: 3 ≥ x
Test Value:
3 ≥ 0
TRUE
FALSE
Test Value:
3 ≥ 4 -3 3
Example 5: x = ½
FALSE
Test Value:
0 = ½
FALSE -½
Test Value:
1 = ½
Example 6: x  ¼
Test Value:
0 ≠ ¼
TRUE
TRUE
Test Value:
1 ≠ ¼ -¼

5. II. Graphing Inequalities
Example 7: 4 > X > -5
FALSE
TRUE
FALSE -5 -4 4 5
Test Value:
4 > -6 > -5
Test Value:
4 > 0 > -5
Test Value:
4 > 5 > -5
Example 8: -9 ≤ X ≤ -4 F T F -9 -4 4 9
Test Value:
-9 ≤ -10 ≤ -4
Test Value:
-9 ≤ -5 ≤ -4
Test Value:
-9 ≤ 0 ≤ -4

6. II. Graphing Inequalities
Example 9: x > 3 or x < -2
TRUE
FALSE
TRUE -3 -2 2 3
Test Value:
-4 > 3 or -4 < -2
Test Value:
0 > 3 or 0 < -2
Test Value:
4 > 3 or 4 < -2
Example 10: -2 ≥ x or 1 ≤ x
TRUE
FALSE
TRUE -2 -1 1 2
Test Value:
-2 ≥ -3 or 1 ≤ -3
Test Value:
-2 ≥ 0 or 1 ≤ 0
Test Value:
-2 ≥ 2 or 1 ≤ 2