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Linear Inequation


Inequalities

An inequality is a mathematical statement which states whether one quantity is less than or greater than another quantity.
    Inequalities are of four types
  1. a is greater than b; a>b
  2. a is greater then or equal to b; a≥b
  3. a is less than b; a<b
  4. a is less than or equal to b; a≤b

Linear Inequations

A linear equations is one of the following
    A linear inequation is one of the following
  1. ax + b > 0
  2. ax + b ≥ 0
  3. ax + b < 0
  4. ax + b ≤ 0
  5. where a and b are real numbers and a≠0
The set from which values of the variable involved in the inequation are chosen is called the replacement set.
The values from the replacement set which makes the inequations true are called solutions of the inequations and the set is called the solution set of the inequation.

Inequality postulates

  1. Adding or subtracting a non-zero number from both sides of the inequality produces an equivalent inequality.
  2. Multiplying or dividing both sides of an inequality by a non-zero positive number produces an equivalent inequality.
  3. Multiplying or dividing both sides of an inequality by a non-zero negative number produces a reversed inequality.



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