Section 6.5: Inequalities

6.5 Outline

  1. Comparison property
  2. 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. 1. multiply both sides by a negative number.
  2. divide both sides by a negative number.
  3. interchange the x and y.