NCERT Solutions for Exercise 6.2 Class 11 Maths Chapter 6 - Linear Inequalities

# NCERT Solutions for Exercise 6.2 Class 11 Maths Chapter 6 - Linear Inequalities

Edited By Vishal kumar | Updated on Nov 06, 2023 01:34 PM IST

## NCERT Solutions for Class 11 Maths Chapter 6: Linear Inequalities Exercise 6.2- Download Free PDF

NCERT Solutions for Class 11 Maths Chapter 6: Linear Inequalities Exercise 6.2- NCERT solutions for exercise 6.2 Class 11 Maths Chapter 6 discusses questions from the topic of graphical solutions of linear inequalities in two variables. Exercise 6.2 Class 11 Maths questions related to linear inequalities in two-dimensional planes graphically. One example of the question type is given in the NCERT solutions for Class 11 Maths chapter 6 exercise 6.2 is “solve graphically; x+2y<5. The concepts of solution region, solution set, identification of half-plane etc can be practised through Class 11 Maths chapter 6 exercise 6.2. The questions in NCERT syllabus Class 11th Maths chapter 6 exercise 6.2 are single two-variable inequalities. The system of inequalities in 2 variables is discussed in the session after Class 11 Maths Chapter 6 Exercise 6.2.

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The following practice exercises are also discussed in the NCERT book chapter linear inequalities along with exercise 6.2 Class 11 Maths which are developed by subject matter experts. They are presented in an easy-to-understand language, and each question is explained in comprehensive detail. In addition to text solutions, PDF versions are also available, enabling students to use them according to their convenience, without requiring an internet connection, and all of this is provided free of charge.

**As per the new CBSE Syllabus for 2023-24, this chapter has been assigned a different number, and it is now referred to as Chapter 5.

## Access Linear Inequalities Class 11 Chapter 6 Exercise 6.2

Graphical representation of $x+y=5$ is given in the graph below.

The line $x+y=5$ divides plot in two half planes.

Select a point (not on line $x+y=5$ ) which lie in one of the half planes, to determine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

$1+2< 5$ i.e. $3< 5$ , which is true.

Therefore, half plane (above the line) is not a solution region of given inequality i.e. $x + y < 5$ .

Also, the point on the line does not satisfy the inequality.

Thus, the solution to this inequality is half plane below the line $x+y=5$ excluding points on this line represented by the green part.

This can be represented as follows:

$2x + y \geq 6$

Graphical representation of $2x+y=6$ is given in the graph below.

The line $2x+y=6$ divides plot in two half-planes.

Select a point (not on the line $2x+y=6$ ) which lie in one of the half-planes, to determine whether the point satisfies the inequality.

Let there be a point $(3,2)$

We observe

$6+2\geq 6$ i.e. $8\geq 6$ , which is true.

Therefore, half plane II is not a solution region of given inequality i.e. $2x + y \geq 6$

Also, the point on the line does satisfy the inequality.

Thus, the solution to this inequality is the half plane I, above the line $2x+y=6$ including points on this line , represented by green colour.

This can be represented as follows:

$3x + 4y \leq 12$

Graphical representation of $3x + 4y = 12$ is given in the graph below.

The line $3x + 4y = 12$ divides plot into two half-planes.

Select a point (not on the line $3x + 4y = 12$ ) which lie in one of the half-planes, to determine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

$1+2\leq 12$ i.e. $3\leq 12$ , which is true.

Therefore, the half plane I(above the line) is not a solution region of given inequality i.e. $3x + 4y \leq 12$ .

Also, the point on the line does satisfy the inequality.

Thus, the solution to this inequality is half plane II (below the line $3x + 4y = 12$ ) including points on this line, represented by green colour.

This can be represented as follows:

$y + 8 \geq 2x$

Graphical representation of $y + 8 = 2x$ is given in the graph below.

The line $y + 8 = 2x$ divides plot in two half-planes.

Select a point (not on the line $y + 8 = 2x$ ) which lie in one of the half-planes, to determine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

$2+8\geq 2\times 1$ i.e. $10\geq 2$ , which is true.

Therefore, half plane II is not solution region of given inequality i.e. $y + 8 \geq 2x$ .

Also, the point on the line does satisfy the inequality.

Thus, the solution to this inequality is the half plane I including points on this line, represented by green colour.

This can be represented as follows:

$x - y \leq 2$

Graphical representation of $x - y =2$ is given in the graph below.

The line $x - y =2$ divides plot in two half planes.

Select a point (not on the line $x - y =2$ ) which lie in one of the half-planes, to determine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

$1-2\leq 2$ i.e. $-1\leq 2$ , which is true.

Therefore, half plane Ii is not solution region of given inequality i.e. $x - y \leq 2$ .

Also, the point on the line does satisfy the inequality.

Thus, the solution to this inequality is the half plane I including points on this line, represented by green colour

This can be represented as follows:

$2x - 3y > 6$

Graphical representation of $2x - 3y = 6$ is given in the graph below.

The line $2x - 3y = 6$ divides plot in two half planes.

Select a point (not on the line $2x - 3y = 6$ )which lie in one of the half-planes, to determine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

$2-6> 6$ i.e. $-4 > 6$ , which is false .

Therefore, half plane I is not solution region of given inequality i.e. $2x - 3y > 6$ .

Also point on line does not satisfy the inequality.

Thus, the solution to this inequality is half plane II excluding points on this line, represented by green colour.

This can be represented as follows:

$-3x + 2y \geq -6$

Graphical representation of $-3x + 2y = -6$ is given in the graph below.

The line $-3x + 2y = -6$ divides plot in two half planes.

Select a point (not on the line $-3x + 2y = -6$ ) which lie in one of the half planes, to determine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

$-3+4\geq -6$ i.e. $1\geq -6$ , which is true.

Therefore, half plane II is not solution region of given inequality i.e. $-3x + 2y \geq -6$ .

Also, the point on the line does satisfy the inequality.

Thus, the solution to this inequality is the half plane I including points on this line, represented by green colour

This can be represented as follows:

$3y - 5x < 30$

Graphical representation of $3y - 5x =30$ is given in graph below.

The line $3y - 5x =30$ divides plot in two half planes.

Select a point (not on the line $3y - 5x =30$ ) which lie in one of the half plane , to detemine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

$6-5< 30$ i.e. $1< 30$ , which is true.

Therefore, half plane II is not solution region of given inequality i.e. $3y - 5x < 30$ .

Also point on the line does not satisfy the inequality.

Thus, solution to this inequality is half plane I excluding points on this line, represented by green colour.

This can be represented as follows:

$y < -2$

Graphical representation of $y=-2$ is given in graph below.

The line $y < -2$ divides plot in two half planes.

Select a point (not on the line $y < -2$ ) which lie in one of the half plane , to detemine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

i.e. $2< -2$ , which is false.

Therefore, the half plane I is not a solution region of given inequality i.e. $y < -2$ .

Also, the point on the line does not satisfy the inequality.

Thus, the solution to this inequality is half plane II excluding points on this line, represented by green colour.

This can be represented as follows:

$x > - 3$

Graphical representation of $x=-3$ is given in the graph below.

The line $x=-3$ divides plot into two half-planes.

Select a point (not on the line $x=-3$ ) which lie in one of the half-planes, to determine whether the point satisfies the inequality.

Let there be a point $(1,2)$

We observe

i.e. $1> -3$ , which is true.

Therefore, half plane II is not a solution region of given inequality i.e. $x > - 3$ .

Also, the point on the line does not satisfy the inequality.

Thus, the solution to this inequality is the half plane I excluding points on this line.

This can be represented as follows:

## More About NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2

Examples 9 to 11 are illustrated in the NCERT book before exercise 6.2 Class 11 Maths for understanding the steps followed in solving problems. After going through these examples, students can practice Class 11 Maths Chapter 6 exercise 6.2. In the NCERT solutions for Class 11 Maths chapter 6 exercise 6.2 there are ten questions. All the 10 questions of Class 11th Maths chapter 6 exercise 6.2 are to solve inequalities graphically in a two-dimensional plane.

Also Read| Linear Inequalities Class 11th Notes

## Benefits of NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2

• The questions in exercise 6.2 Class 11 Maths help to understand the graphical method of solving linear inequalities in two variables.

• Also, students can expect questions from Class 11 Maths Chapter 6 exercise 6.2 for their final exams

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## Key Features of NCERT 11th Class Maths Exercise 6.2 Answers

1. Step-by-step solutions: Detailed, step-by-step explanations for each 11th class maths exercise 6.2 answers to facilitate an understanding of mathematical concepts and problem-solving techniques.

2. Clarity and accuracy: Ex 6.2 class 11 solutions are presented clearly and accurately, helping students prepare for exams with confidence and improve their comprehension.

3. Curriculum alignment: Class 11 maths ex 6.2 solutions closely adhere to the NCERT curriculum, covering topics and concepts as per the official syllabus.

4. Accessibility: These class 11 ex 6.2 solutions are often available for free, making them easily accessible to students.
5. Format options: PDF versions of the class 11 maths chapter 6 exercise 6.2 is provided, allowing students to download and use them conveniently, both online and offline.

Also see-

## Subject Wise NCERT Exampler Solutions

1. Mention the number of exercises solved in the Class 11 NCERT Maths chapter linear inequalities

4 exercises are solved including the miscellaneous exercises.

2. How many questions are discussed in the NCERT solutions for Class 11 Maths chapter 6 exercise 6.2?

Ten questions.

3. What is the solution region?

The area which contains all the solutions of inequality is called the solution region.

4. What happens when both sides of an inequality are multiplied by a negative number?

The inequality is reversed.

5. What is the difference between x less than n and x less than or equal to n on the number line?

For x<n there will be a circle on the number n and for x less than or equal to n there will be a dark circle on the number n.

6. What topic is covered in exercise 6.2 Class 11 Maths?

Linear inequalities in one variable, their formation and solution

7. Solve 30x<90

30x<90

divide both sides with 30, then we get

x<30; which is the required solution and can be represented graphically by a dark line left to the number 30 and a circle on 30(i.e without including 30) on a number line

8. Solve -30x<90

Divide both sides with 30

-x<30

Multiply both sides by -1 (the inequality sign get reversed)

x>-30 is the solution. This can be represented on a number line by a dark line to the right of -30 with a circle on -30

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