LINEAR INEQUALITIES AND ITS REPRESENTATION

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Definition of linear inequality
 A statement involving two real numbers or two algebraic expressions related by the symbol ' < ', ' > ', ' ≤ ', ' ≥ ' form an inequality.

Types of inequalities

  • Numerical inequalities, e.g. 7 > 5, 11 < 8 etc.
  • Literal inequalities, e.g. x < 7, y > 4, x ≥  6 etc.
  • Double inequalities, e.g. 3 ≤ x < 5, 6 < y < 11 etc.
  • Strict inequalities, e.g. x < 7, ax + by > 0 etc.
  • Slack inequalities, e.g. ax + by ≤ 0
  • Quadratic inequalities, e.g. ax^2 + bx + c > 0 etc.
Rules for solving an inequality

  • Rule 1: Equal numbers may be added to ( or subtracted from ) both sides of an inequality without affecting the sign of inequality.
  • Rule 2: Both sides of an inequality can be multiplied ( or divided ) by the same positive number. But when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed.
Representation of inequality on real number line

LINEAR INEQUALITIES AND ITS REPRESENTATION

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