1. 1.5: Solving Inequalities

2. Key Concepts For any real numbers a, b, and c, if a > b, then:
Addition Property: a+c > b+c
Subtraction Property: a-c < b-c
And if c ≠ 0,
Multiplication Property: when c > 0, ac > bc; when c < 0, ac < bc
Division Property: when c > 0, (a/c) > (b/c); when c<0, (a/c) < (b/c)
And vise versa ( for a < b).
Graphing: Open circle means the solution does not include the point; Closed circol means the solution includes the point.

3. Examples of Simple Inequalities
Example Graph

4. Examples of more complicated multi-step inequalities
-4x < (8x + 40)/ 3
-12x < 8x + 40
-20x < 40
x > -2
-7x + 80 < 3x -64
-10x < -144
x > 14.4
Example Graph

5. Practice Problems x + 2 > 5 x - 7 < -4 8x < 6 128x > 256
Answers:
x > 3
x < 3
x < ¾
x > 2
x < 20
x < 4