Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Inequalities and Linear inequalities

Inequalities:

Two real numbers or two algebraic expressions related by the symbols <,>, \leq \text { or} \geq form an inequality.

For examples: 

3x <20, \qquad 4x+2y>5,\qquad 2<5

Linear Inequality:

An inequality is said to be linear if each variable occurs in the first degree only and there is no term involving the product of the variables.

For examples: 

 ax+b<0, \qquad ax+b \leq 0 etc.

Open Interval:

If  a & b are real numbers, such that  a <b then the set of all real numbers  x such that  a<x<b is called an open interval and is denoted by  (a,b) .

Therefore (a,b)=\{x: a < x < b, x \in R\}

Closed Interval:

If  a  b are real numbers such that  a <b , then the set of all real numbers  x such that  a \leq x \leq b is called a closed interval and is denoted by [a,b] .

Therefore  [a,b] =\{x: a\leq x \leq b, x \in R\}

Solution of an inequality:

The value of  x , which make an inequality a true statement, are called solutions of the inequality.

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