NCERT Solutions Class 11 Mathematics Chapter 6- Linear Inequalities
Class 11 is the foundation for Class 12. The NCERT Solutions Class 11 Mathematics Chapter 6 is dependable and has been curated in a very simple and precise format. The solutions cover all the answers to the textual questions including all the concepts of the chapter. With the help of the Class 11 Mathematics Chapter 6 solutions , students fetch excellent marks in their exams as well as competitive entrance examinations such as JEE Mains and JEE Advanced. NCERT Solutions offer thorough and quick revision before the exams.
The NCERT Solutions Class 11 Mathematics Chapter 6 discusses the various concepts related to Linear Inequalities. To clearly understand all concepts of this chapter, students must refer to the NCERT Solutions Class 7 and NCERT Solutions Class 8 to recall all the related concepts. The NCERT Solutions Class 11 Mathematics Chapter 6 provides solved key to textual questions which clears the conceptual understanding of the students which finally helps them to gain high scores in the examinations. Using these solutions, they can comprehend all theorems, sums and formulas from this chapter. Students must consider using Chapter 6 Class 11 Mathematics solutions provided by Extramarks for effective preparation.
Key Topics Covered in NCERT Solutions Class 11 Mathematics Chapter 6
The subject matter experts at Extramarks have covered the following key topics in the Chapter 6 Mathematics Class 11 solutions through detailed research and analysis:
| Exercise |
Topic |
| 6.1 |
Introduction |
| 6.2 |
Inequalities |
| 6.3 |
Algebraic Solutions of Linear Inequalities and Graphical Representation |
| 6.4 |
Solutions of the Linear Inequalities in Two Variables using graphs |
| 6.5 |
Solution of System of Linear Inequalities |
Introduction:
In this Chapter 6, Mathematics Class 11, students will study linear equalities. The previous knowledge about equations in one and two variables studied introduced in the NCERT solutions Class 9 and NCERT solutions Class 10 is used in this Chapter. In NCERT Solutions Class 11 Mathematics Chapter 6, students will learn to translate statement problems in the equation format, using signs of inequalities such as less than (<), greater than (>), less than equal to (), and greater than equal to ().
The study of NCERT Solutions Class 11 Mathematics Chapter 6 is very useful in the field of science, optimisation problems, statistics, etc.
Inequalities:
Students will learn about the term ‘inequality’, which is the relation between two real numbers or algebraic expressions. They will also gain understanding about the different types of inequalities, such as numerical inequalities, literal inequalities and double inequalities. A complete explanation is given in the NCERT Solutions Class 11 Mathematics Chapter 6 with the help of several examples of inequalities. Students will also understand the difference between strict inequalities and slack inequalities.
Algebraic Solutions of Linear Inequalities and Graphical Representation:
In this section, students gain knowledge about the left-hand side (LHS) and right-hand side (RHS) of the inequalities. They will also learn about the solutions and the solution set of the inequalities. A true statement is also defined in this section. It also recalls the rules for solving a linear equation. Similarly, rules for solving linear inequalities with solved examples are also mentioned in this part. In the Chapter 6 Class 11 Mathematics, students will also learn about visual representation using graphs of inequalities in one variable.
Students must refer to the NCERT Solutions Class 11 Mathematics Chapter 6 for practising several questions.
Graphical Solution of Linear Inequalities with Two Variables:
In this section, students will learn to draw a graph and represent the relation between inequalities of two variables. Concepts such as the half-planes and their types (lower and upper half-planes) are discussed in this chapter. Students will learn to solve sums based on the three possibilities, namely:
(i) ax + by = c
(ii) ax + by > c
(iii) ax + by < c
The solution region is defined in this section. Several examples are included to explain the procedure for solving linear inequalities in two variables.
- The solution region contains all the solutions to the linear inequality.
- To identify the half-plane, which is represented by the linear inequality, it is necessary to take the point (a, b) and check if it satisfies the inequality or not. If it satisfies, then the inequality will represent the half-plane and shade the solution region which contains the point.
- If the linear inequality is of the form ax + by > c or of the form ax + by < c, then any points on the line ax + by = c are also included in the solution region. Draw a dark line in the solution region.
- If the linear inequality is of the form ax + by > c or of the form ax + by < c, then any points on the line ax + by = c will not be included in the solution region. Draw a broken or dotted line.
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NOTE:
- Any point which lies in the half-plane II satisfies ax + by > c.
- Any point satisfying the inequality ax + by > c lies in half-plane II.
- If b < 0, then the point which satisfies ax + by > c lies in the half-plane I.
- All points satisfying ax + by > c lies in half-planes II or I as b > 0 or b < 0.
- The graph of inequality ax + by > c will be the half-plane (solution region). It is represented by shading.
Solution of System of Linear Inequalities:
In the previous section, students learnt to solve linear inequalities involving one or two variables using graphs. In this section, they will learn to illustrate the method for solving a system of linear inequalities in two variables.
NCERT Solutions Class 11 Mathematics Chapter 6: Exercise & Solutions
The NCERT Solutions Class 11 Mathematics Chapter 6 Linear Inequalities are available for students on the Extramarks’ mobile application and website . The notes comprehensively explain and provide detailed answers to all the textual questions included in the Chapter 6 Class 11 Mathematics. Several solved examples are used to explain the practical applications of linear inequalities. The NCERT Solutions for Class 11 Mathematics Chapter 6 help students to revise all important formulas, derivations and key points. With knowledge of Class 11 Mathematics Chapter 6, students will be able to tackle all difficult questions asked in the examinations.
Click on the below links to learn and practice the Extramarks NCERT Solutions Class 11 Mathematics Chapter 6:
Students can also gain access to the other study materials like the revision notes, CBSE sample papers and mock tests. Students who are preparing for the board exams are advised to use the NCERT Solutions Class 11 Mathematics Chapter 6 from our Extramarks’ website. They can also go through several NCERT reference books for preparing efficiently.
- NCERT Solutions Class 1
- NCERT Solutions Class 2
- NCERT Solutions Class 3
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
NCERT Exemplar Class 11 Mathematics
The NCERT Exemplar Mathematics notes are an important study material which students must refer to. It includes all detailed explanations and helps students to gain an in-depth understanding of all complex topics. Students can also practice several challenging questions from the chapter. Using the Exemplar notes along with NCERT Solutions Class 11 Mathematics Chapter 6 will help students to enhance their problem-solving and thinking abilities. The study materials on the Extramarks platform will help students prepare for board exams such as JEE Mains, IIT, etc.
The platform of Extramarks provides the best learning experience to all students. Through the best study notes, we provide guidance and support to enable academic progress. Students are advised to practice and study using the all-inclusive NCERT Solutions Class 11 Mathematics Chapter 6 and solve many sample papers and past years’ question papers.
Key Features of NCERT Solutions Class 11 Mathematics Chapter 6
- The NCERT Solutions Class 11 Mathematics Chapter 6 explains all concepts in a detailed manner using proper logic and reasoning.
- Students will learn tips, tricks and methods to solve problems quickly and easily.
- The NCERT Solutions Class 11 Mathematics Chapter 6 is based on the CBSE syllabus and follow the latest guidelines by the CBSE.
- Students can prepare for board exams and annual examinations effectively.
- These notes help to clarify all doubts by providing detailed and accurate answers to the chapter end exercises. This enables students to solve the questions and cross-check their answers with an authentic source. By practising through NCERT Solutions Class 11 Mathematics Chapter 6, students will gain confidence and problem-solving abilities.