o o
The notation a ≤ b means that a is less than or equal to b The notation a ≥ b means that a is greater than or equal to b
Types of Inequalities:
o Numerical inequalities: Relationship between numbers. E. g. 3 < 5 o Literal or variable inequalities: Relationship between variables or variable & number. g. x < 5 o Double Inequalities: Relationship from two side. E. g. 2 < x < 5 o Strict inequalities: An inequality that uses the symbols < or >. The symbols ≤ and ≥ are not used. g. x < 5; 3 < 5 o Slack inequalities. An inequality that uses the symbols ≤ or ≥ E. g. x ≤ 5 o Linear inequalities in one variable: An inequality which involves a linear function in one variable E. g. x < 5; o Linear inequalities in two variables: An inequality which involves a linear function in two variable E. g. 3x + 2y < 5; o Quadratic inequalities: An inequality which involves a quadratic function. E. g. x 2 + 2x ≤ 5
Solution for linear inequality in one variable Solution & Solution Set Solution: Values of x, which make inequality a true statement. E. g. 3 is a solution for x < 7 Solution Set: The set of values of x is called its solution set. E. g.: 1,2,3,4,5,6 is solution set for x < 7 where x is natural Number
Rules of Inequality:
o Equal numbers may be added to( or subtracted from) both sides of an inequality without affecting the sign of inequality. E. g. x < 7 is same as x + 2 < 7 + 2
o Both sides of an inequality can be multiplied( or divided) by the same positive number without affecting the sign of inequality. E. g.: x + y < 7 is same as( x + y) * 3 < 7 * 3 o But when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed g.: x + y < 7 is same as( x + y) *(- 3) > 7 *(- 3)