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CBSE NOTES ⇒ Class 11th ⇒ Mathematics ⇒ 6. Linear Inequalities

## 6. Linear Inequalities

### Introduction

Inequalities:

Definition: Two real numbers or algebraic expressions related by symbol '<', '>', '≤' or '≥', such relations which are made by these symbols is called inequalities.

symbols:

< { less than}

> { greater than}

≤ { less than or equal to}

≥ { greater than or equal to}

Type of Inequalities: ( On the basis of variable and Numerical)

(i) Numerical Inequalities: The Inequalities which has both side numeric value.

Examples:

6 < 9

3 > 1

3 < 5

1 > 0

(ii) Literal Inequalities: The Inequalities which have variables is called literal Inequalities.

Examples:

x < 5

x > 7

≤ 7

x ≥ 3

Important rules:

Rule (i) Equal munbers may be added to or subtracted from both sides of an inequality without affecting the sign of imequality.

Rule (ii) Both sides of an imequality can be multiplied or divided by the same posiitive number. But, When both sides are multiplied or divided by a negative number then the sign of inequality is reversed.

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