Equations and Inequalities

1
Equations and Inequalities

• 8/18/09

2
Warm-Up

• Solve
• 5(3 2x) 12 4(x 6)

3
Solving Equations

1. Distribute
2. Clear fractions
3. Collect like terms on both sides
4. Use addition/subtraction to get variable alone
5. Use multiplication/division

4
Clearing Fractions

• We can clear an equation of fractions by
  multiplying all terms by the least common
  denominator.
• Example

5
Examples

• 1.
• 2.

6
Zero Product Property

• For any real numbers a and b,
• ab 0 iff a b or b 0

7

• If x 0 and y 0, must xy 0?
• If x 0 or y 0, must xy 0?
• If xy 0, must x 0 and y 0?

8
Examples

1. (a 3)(a 1) 0
2. (2x 4)(3x 15) 0
3. 5(x 8)(x 2)