Inequality Symbols

An inequality is a statement that uses one of the following symbols:

  • = equal to
  • ≠ not equal to
  • ≅ approximately equal to
  • > greater than
  • ≥ greater than or equal to
  • < less than
  • ≤ less than or equal to

Mathematical Operations

Inequalities are manipulated algebraically the same way as equations with one exception: Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

Properties of Positive & Negative Numbers

  1. The product of positive numbers is positive.
  2. The product of a positive number and a negative number is negative.
  3. The product of an even number of negative numbers is positive.
  4. The product of an odd number of negative numbers is negative.
  5. The sum of negative numbers is negative.

Transitive Property

If x < y  and y < z, then x < z

Addition of Like Inequalities

If x < y and w < z, then x+w < y+z