# OP Malhotra Class-11 Inequalities S.Chand ISC Maths Solutions

OP Malhotra Class-11 Inequalities S.Chand ISC Maths Solutions Chapter-11. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-11 (a), 11 (b), 11 (c) With Chapter Test. Visit official Website for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Class-11 Inequalities S.Chand ISC Maths Solutions

 Class: 11th Subject: Mathematics Chapter  : Ch-11 Inequalities of Section -A
 Board ISC Writer OP Malhotra Publications S.Chand Publications 2020-21

-: Select Topics :-

Exe-11 (a)

Exe-11 (b)

Exe-11( c)

Chapter Test

### OP Malhotra Class-11 Inequalities S.Chand ISC Maths Solutions

Introduction

In the earlier classes, we have studied the linear equations in one or two variables. In class 11, linear inequalities, we are going to learn about the linear inequalities in one variable, two variables with its algebraic solution and graphical solution. The linear inequalities are used to solve the problems in different fields like Science, Engineering, Mathematics, and so on.

Inequalities

Two algebraic expressions or real numbers related by the symbol ≤, ≥, < and > form an inequality. For example: px + qy > 0, 9a – 21b < 0, etc. Equal numbers can be subtracted or added from both the sides of an inequality equation. Also, both sides of an inequality can be divided or multiplied by the same number (non-zero). If both sides of an inequality are divided by the negative number, then the inequality equation gets reversed. The solution of the inequality is the value of x, which makes inequality a true statement.

#### Rules for solving an Inequality

• We can add or subtract the same number to LHS and RHS of inequality without changing the sign of that inequality.
• We can divide or multiply both sides of an inequality by the same positive number.
• The sign of the inequality is reversed when both sides (LHS and RHS) are divided or multiplied by the same negative number.

For solving the inequalities we follow the same rules except with a difference that the sign of inequality is reversed (< to > and ≤ to ≥) whenever an inequality is divided or multiplied by a -ve number. Some examples of inequalities are:

• Strict inequalities: ax + b < 0, ax + b > 0, ax + by < c, a+bx+c>0
• Slack inequalities: ax + b ≤ 0, ax + b ≥ 0, ax + by ≤ c, ax + by ≥ c, a+bx+c0
• Linear inequalities in one variable: ax + b < 0 ax + b > 0, ax + b ≤ 0 ax + b ≥ 0 [when a ≠ 0]
• Linear inequalities in two variable: ax + by < c, ax + by > c, ax + by ≤ c, ax + by ≥ c.

Exe-11 (a)

### OP Malhotra Class-11 Inequalities S.Chand ISC Maths Solutions

Page 11-7 to 11-9

### Exe-11 (b)

OP Malhotra Class-11 Inequalities S.Chand ISC Maths Solutions

Page 11-18 to 11-19

### Exe-11 (c)

OP Malhotra Inequalities S.Chand ISC Maths Solutions

Page 11-27

Chapter Test

### OP Malhotra Class-11 Inequalities S.Chand ISC Maths Solutions

Page 11-28

-: End of Inequalities Solution :-

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1. No solution for inequality p

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