# CBSE Class 11 Mathematics Linear Inequalities Notes

Download CBSE Class 11 Mathematics Linear Inequalities Notes in PDF format. All Revision notes for Class 11 Mathematics have been designed as per the latest syllabus and updated chapters given in your textbook for Mathematics in Class 11. Our teachers have designed these concept notes for the benefit of Class 11 students. You should use these chapter wise notes for revision on daily basis. These study notes can also be used for learning each chapter and its important and difficult topics or revision just before your exams to help you get better scores in upcoming examinations, You can also use Printable notes for Class 11 Mathematics for faster revision of difficult topics and get higher rank. After reading these notes also refer to MCQ questions for Class 11 Mathematics given on studiestoday

## Revision Notes for Class 11 Mathematics Chapter 6 Linear Inequalities

Class 11 Mathematics students should refer to the following concepts and notes for Chapter 6 Linear Inequalities in Class 11. These exam notes for Class 11 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks

### Chapter 6 Linear Inequalities Notes Class 11 Mathematics

Class XI

Chapter Notes

Linear Inequalities

Definitions

1. Two real numbers or two algebraic expressions related by the symbol ‘<’, ‘>’, ‘≤’ or ‘≥’ form an inequality.

2. Inequalities containing ‘<’, or ‘>’ are called strict inequalities.

3. Inequalities containing ‘≤’ or ‘≥’ are called slack inequalities.

4. An inequality containing any two of‘<’, ‘>’, ‘≤’ or ‘≥’is called double inequality.

5. Solution of an inequality in one variable is the value of the variable which makes it a true statement

6. A linear expression in one variable involving the inequality symbol is linear inequality in one variable. General forms:

ax + b < 0 (1)

ax + b > 0 (2)

ax + b ≤ 0 (3)

ax + b ≥ 0 (4)

7. A linear inequality involving two variables is known as a linear inequality in two variables. General forms

ax + by < c (5)

ax + by > c (6)

ax + by ≤ c (7)

ax + by ≥ c (8)

ax² + bx + c ≤ 0 (9)

ax² + bx + c ≥ 0 (10)

7. The region containing all the solutions of an inequality is called the solution region.

8. The solution region of the system of inequalities is the region which satisfies all the given inequalities in the system simultaneously.

9. Quadratic inequality is quadratic polynomial with inequality sign. Generic quadratic inequality is of the form ax2+bx+c > 0 Concepts

1. If two real numbers are related by the symbols ‘<’, ‘>’, ‘≤’ or ‘≥’ then the inequality is a numerical inequality and in case of algebraic expressions it is literal inequality. 2<3 is numerical inequality 5x+2≤7 is literal inequality

2. Rules for simplifying the inequalities

Rule 1: Equal numbers may be added to (or subtracted from) both sides of an equation.

If a < b then a + c < b + c.

Rule 2: Both sides of an equation may be multiplied (or divided) by the same non – zero number.

If a < b then ac < bc

Rule 3: Sign of inequality is reversed in case of multiplication (or division) by a negative number If a < b then ak > bk, where k is a negative number

Rule 4: Sign of inequality is reversed in case of taking the reciprocals  5. In order to identify the half plane represented by an inequality, take any point (a, b) (not on line) and check whether it satisfies the inequality or not.
If it satisfies, then inequality represents the half plane and shade the region which contains the point, otherwise, the inequality represents the half plane which does not contain the point within it. For convenience, the point (0, 0) is preferred.

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### CBSE Class 11 Mathematics Chapter 6 Linear Inequalities Notes

We hope you liked the above notes for topic Chapter 6 Linear Inequalities which has been designed as per the latest syllabus for Class 11 Mathematics released by CBSE. Students of Class 11 should download and practice the above notes for Class 11 Mathematics regularly. All revision notes have been designed for Mathematics by referring to the most important topics which the students should learn to get better marks in examinations. Studiestoday is the best website for Class 11 students to download all latest study material.

### Notes for Mathematics CBSE Class 11 Chapter 6 Linear Inequalities

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#### Chapter 6 Linear Inequalities Notes for Mathematics CBSE Class 11

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#### Chapter 6 Linear Inequalities CBSE Class 11 Mathematics Notes

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#### Notes for CBSE Mathematics Class 11 Chapter 6 Linear Inequalities

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