6.5 Outline

A. Comparison property
B. Solving linear inequalities
      1. inequality symbol
      2. inequality
      3. addition property of inequality
      4. multiplication property of inequality
      5. procedure for solving a linear inequality

6.5 Essential Ideas

Comparison Property
For any two numbers x and y, exactly one of the following is true:
      1.  x = y    x is equal to y (the same as)
      2.  x > y    x is greater than y (larger than)
      3.  x < y    x is less than y (smaller than).

Given x < y, x <= y, x > y, or x >= y:
The inequality symbols are the same if you
      1.  add the same number to both side.
      2.  subtract the same number from both sides.
      3.  multiply both sides by a positive number.
      4.  divide both sides by a positive number.
The inequality symbols are reversed if you
      1.  multiply both sides by a negative number.
      2.  divide both sides by a negative number.
      3.  interchange the x and y.