1. Solving Inequalities Using Multiplication and Division
Algebra 1: Section 3-3
Solving Inequalities Using Multiplication and Division

2. Objectives: To use multiplication to solve inequalities
To use division to solve inequalities

3. Multiplication Properties:
Multiplication, c>0
Multiplication, c<0
For every real number a and b, and for c>0,
If a>b, then ac>bc
Example: 4> -1, so (5) > (-1)(5)
If a<b, then ac<bc
Example: -6<3, so
(-6)(5) < (3)(5)
For every real number a and b, and for c<0,
If a>b, then ac<bc
Example: 4> -1, so (-2) < (-1)(-2)
If a<b, then ac>bc
Example: -6<3, so
(-6)(-2) > (3)(-2)

4. Division Properties Division, c > 0 Division, c < 0
For every real number a and b, and for c>0
If a>b, then a/c>b/c
Example: 6>4, so /2>4/2
If a<b, then a/c<b/c
Example: 2<8, so 2/2<8/2
For every real number a and b, and for c<0
If a>b, then a/c<b/c
Example: 6>4, so /-2<4/-2
If a<b, then a/c>b/c
Example: 2<8, so 2/-2>8/-2

5. Using the Multiplication Property
Multiply by a positive
Solve: d > 5
3 6
Multiply by a negative
Solve: - t < 1 2

6. Using the Division Property
Solve: -3w > 12
Solve: 5n < -25

7. Assignment
Pg. 149: multiples of 3 (#3-54, 60-72),
82, 83