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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.

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This Story also Contains
  1. NCERT Class 11 Maths Chapter 6 notes
  2. Algebraic Solutions Of Linear Inequalities In One Variable And Their Graphical Representation
  3. Graphical Solution Of Linear Inequalities In Two Variables
  4. Significance of NCERT Class 11 Math Chapter 6 Notes
  5. NCERT Class 11 Notes Chapter Wise.

After going through Class 11 Linear Inequalities notes

Also, students can refer,

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.

1647258759177

  • 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.

1647258969619

This is all about this chapter.

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.

Linear inequalities Class 11 notes pdf download: link

NCERT Class 11 Notes Chapter Wise.

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