Linear Inequalities Class 11th Notes - Free NCERT Class 11 Maths Chapter 6 notes - Download PDF

# Linear Inequalities Class 11th Notes - Free NCERT Class 11 Maths Chapter 6 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 04:48 PM IST

Linear Inequalities refers to the 6 chapter of NCERT. The NCERT Class 11 Maths chapter 6 notes contain important formulas. Class 11 Math chapter 6 notes contain systematic explanations of topics using examples and exercises. A Class 11 Maths chapter 6 note includes FAQ’s or frequently asked questions about the chapter. Notes for Class 11 Maths chapter 6 NCERT Notes for Class 11 Maths chapter 6 is explained in a simple and understanding way that can reach students easily.

JEE Main Scholarship Test Kit (Class 11): Narayana | Physics WallahAakash Unacademy

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After going through Class 11 Linear Inequalities notes

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## NCERT Class 11 Maths Chapter 6 notes

Linear Inequalities

A linear inequality is defined as the expression where any two values are compared by the inequality symbol such as < > ≤ ≥

Let us take an example

Ram has Rs 120 and wants to buy some bats and balls. The cost of one register is Rs 40 and that of a pen is Rs 20. In this case, if x denotes the number of bats and y, the number of balls which Ram buys, then the total amount spent by her is Rs (40x + 20y) and we have

40x + 20y ≤ 120

## Algebraic Solutions Of Linear Inequalities In One Variable And Their Graphical Representation

Equal numbers may be subtracted from or added to both sides of an inequality without affecting the inequality sign.

Example:

Solve 5x – 3 < 3x +1

when (i) x is an integer

(ii) x is a real number.

Solution:

We have,

5x –3 < 3x + 1

or 5x –3 + 3 < 3x +1 +3 (Rule 1)

or 5x < 3x +4

or 5x – 3x < 3x + 4 – 3x (Rule 1)

or 2x < 4 or x < 2 (Rule 2)

When x is an integer, the solutions of the given inequality are ...,

– 4, – 3, – 2, – 1, 0, 1

When x is a real number, the solutions of the inequality are given by x < 2, i.e., all real numbers x which are less than 2

Therefore, the solution set of the inequality is x ∈ (– ∞, 2).

## Graphical Solution Of Linear Inequalities In Two Variables

We know that a line divides the cartesian plane into two parts known as half-plane.

• The region consisting of all the solutions of an inequality is called the solution region.

• If inequality is of the type ax + by ≥ c or ax + by ≤ c, then the points on the line ax + by = c, are also included in the solution region. So draw a dark line in the solution region.

• If inequality is of the form ax + by > c or ax + by < c, then the points on the line ax + by = c, are not to be included in the solution region. So draw a broken or dotted line in the solution region.

## Significance of NCERT Class 11 Math Chapter 6 Notes

Class 11 Linear inequalities notes will help to understand the formulas, statements, rules in detail. Also, Class 11 Math chapter 6 notes also contains previous year’s questions and NCERT textbook pdf. In Class 11 CBSE Maths Syllabuses, it contains FAQ’s or frequently asked questions along with a topic-wise explanation. Class 11 Maths chapter 6 notes pdf download can be used to download offline.

## NCERT Class 11 Notes Chapter Wise.

 NCERT Class 11 Maths Chapter 1 Notes NCERT Class 11 Maths Chapter 2 Notes NCERT Class 11 Maths Chapter 3 Notes NCERT Class 11 Maths Chapter 4 Notes NCERT Class 11 Maths Chapter 5 Notes NCERT Class 11 Maths Chapter 6 Notes NCERT Class 11 Maths Chapter 7 Notes NCERT Class 11 Maths Chapter 8 Notes NCERT Class 11 Maths Chapter 9 Notes NCERT Class 11 Maths Chapter 10 Notes NCERT Class 11 Maths Chapter 11 Notes NCERT Class 11 Maths Chapter 12 Notes NCERT Class 11 Maths Chapter 13 Notes NCERT Class 11 Maths Chapter 14 Notes NCERT Class 11 Maths Chapter 15 Notes NCERT Class 11 Maths Chapter 16 Notes

### Subject Wise NCERT Solutions

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### NCERT Books and Syllabus

 NCERT Book for Class 11 NCERT Syllabus for Class 11

1. Define Linear inequalities according to Class 11 Maths chapter 6 notes.

Two algebraic expressions or real numbers related by any of the symbols ≤, ≥, <, and > form an inequality.

2. What is the real life use of inequality as per NCERT Class 11 Maths CBSE Class 11 chapter 6 notes?

It is the most often used in solving many real-life problems. It can be determined simply by finding how many products should be placed to get the maximum combination.

3. What textbook should be followed?

Class 11 Math chapter 6 textbook should be followed.

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 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

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