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 )