##### VMC VIQ Scholarship Test

ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Edited By Ramraj Saini | Updated on Sep 23, 2023 06:01 PM IST

**NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities **are provided here. These NCERT Solutions are created by expert team at Careers360 keeping in mind of latest syllabus of CBSE 2023-24. In earlier classes, you have studied equations of one variable and two variables and have solved many problems based on this. In this article, you will get linear inequalities class 11 NCERT solutions. Class 11 Mathematics NCERT book will help you understand the concepts in a much easier way. Here you will get NCERT solutions for class 11 also.

**JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | **

**Suggested: ****JEE Main: high scoring chapters | ****Past 10 year's papers**

**Scholarship Test:** **Vidyamandir Intellect Quest (VIQ)**

This Story also Contains

- Linear Inequalities Class 11 Questions And Answers
- Linear Inequalities Class 11 Questions And Answers PDF Free Download
- Linear Inequalities Class 11 Solutions - Important Formulae And Points
- Linear Inequalities Class 11 NCERT Solutions (Intext Questions and Exercise)
- Linear Inequality Example
- NCERT Solutions For Class 11 Mathematics - Chapter Wise
- NCERT Solutions For Class 11- Subject Wise

Many real life problems can be solved by converting a problem into a mathematical equation but some problems like the height of all the members in your family is less than 180 cm, auditorium can occupy at most 120 tables or chairs or both can't be converted into equations. Statements which involve sign ‘’ '>' (greater than), ‘≤’ (less than or equal) and ≥ (greater than or equal), '<' (less than) are known as inequalities. T he concept of inequality is used in formulating the constraints. In NCERT solutions for class 11 maths chapter 6 linear inequalities you will understand questions based on inequalities in one variable and two variables.

**Inequation (Inequality):**

An inequation or inequality is a statement involving variables and the sign of inequality like >, <, ≥, or ≤.

**Symbols used in inequalities:**

The symbol < means less than.

The symbol > means greater than.

The symbol < with a bar underneath ≤ means less than or equal to.

The symbol > with a bar underneath ≥ means greater than or equal to.

The symbol ≠ means the quantities on the left and right sides are not equal to.

**Algebraic Solutions for Linear Inequalities in One Variable:**

Linear inequalities involve expressions with variables and inequality symbols like <, >, ≤, or ≥.

The solution to a linear inequality can be determined using algebraic methods.

Important rules to follow when solving linear inequalities:

Rule 1: Don’t change the sign of an inequality by adding or subtracting the same integer on both sides of an equation.

Rule 2: Add or subtract the same positive integer from both sides of an inequality equation.

**Graphical Representation of Linear Inequalities:**

Linear inequalities can also be represented graphically on a number line.

For example, x > 3 represents all real numbers greater than 3, which can be shaded on the number line to the right of 3.

Similarly, x ≤ -2 represents all real numbers less than or equal to -2, which can be shaded on the number line to the left of -2.

Free download **NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities **for CBSE Exam.

**Class 11 maths chapter 6 question answer - Exercise 6.1 **

**Question:1(i) ** Solve , when * i * s a natural number.

** Answer: **

Given :

Divide by 24 from both sides

* i * s a natural number which is less than 4.167.

Hence, values of x can be

** Question:1(ii) ** Solve , when

** Answer: **

Given :

Divide by 24 from both sides

* i * s are integers which are less than 4.167.

Hence, values of x can be

** Question:2(i) ** Solve , when

x is a natural number.

** Answer: **

Given :

Divide by -12 from both side

* i * s a natural number which is less than - 2.5.

Hence, the values of x do not exist for given inequality.

** Question:2(ii) ** Solve , when

** Answer: **

Given :

Divide by -12 from both side

are integers less than - 2.5 .

Hence, values of x can be

** Question:3(i) ** Solve , when

** Answer: **

Given :

Divide by 5 from both sides

* are * integers less than 2

Hence, values of x can be

** Question:3(ii) ** Solve , when

** Answer: **

Given :

Divide by 5 from both sides

* are * real numbers less than 2

i.e.

** Question:4(i) ** Solve , when

x is an integer.

** Answer: **

Given :

Divide by 3 from both sides

* are * integers greater than -2

Hence, the values of x can be .

** Question:4(ii) ** Solve , when ) is a real number.

** Answer: **

Given :

Divide by 3 from both side

* are * real numbers greater than -2

Hence , values of x can be as

** Question:5 ** Solve the inequality for real .

** Answer: **

Given :

* are * real numbers greater than -4.

Hence, values of x can be as

** Question:6 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers less than -3.

Hence, values of x can be

** Question:7 ** Solve the inequality for real .

** Answer: **

Given :

* are * real numbers less than equal to -3

Hence , values of x can be as ,

** Question:8 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers less than equal to 4

Hence, values of x can be as

** Question:9 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers less than 6

Hence, values of x can be as

** Question:10 ** Solve the inequality for real .

** Answer: **

Given :

* are * real numbers less than -6

Hence, values of x can be as

** Question:11 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers less than equal to 2.

Hence, values of x can be as

** Question:12 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers less than equal to 120.

Hence, values of x can be as .

** Question:13 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers greater than 4

Hence , values of x can be as

** Question:14 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers less than equal to 2.

Hence , values of x can be as

** Question:15 ** Solve the inequality for real x ** **

** Answer: **

Given :

* are * real numbers greater than 4.

Hence, values of x can be as

** Question:16 ** Solve the inequality for real

** Answer: **

Given :

* are * real numbers less than equal 2.

Hence, values of x can be as .

** Question:17 ** Solve the inequality and show the graph of the solution on number line

** Answer: **

Given :

* are * real numbers less than 3

Hence, values of x can be as

The graphical representation of solutions of the given inequality is as :

** Question:18 ** Solve the inequality and show the graph of the solution on number line

** Answer: **

Given :

* are real * numbers greater than equal to -1.

Hence, values of x can be as

The graphical representation of solutions of the given inequality is as :

** Question:19 ** Solve the inequality and show the graph of the solution on number line

** Answer: **

Given :

* are * real numbers greater than -1

Hence, values of x can be as

The graphical representation of solutions of given inequality is as :

** Question:20 ** Solve the inequality and show the graph of the solution on number line

** Answer: **

Given :

* are * real numbers greater than equal to

Hence, values of x can be as

The graphical representation of solutions of the given inequality is as :

** Answer: **

Let x be marks obtained by Ravi in the third test.

The student should have an average of at least 60 marks.

the student should have minimum marks of 35 to have an average of 60

** Answer: **

Sunita’s marks in the first four examinations are 87, 92, 94 and 95.

Let x be marks obtained in the fifth examination.

To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or more in five examinations.

Thus, Sunita must obtain 82 in the fifth examination to get grade ‘A’ in the course.

** Answer: **

Let x be smaller of two consecutive odd positive integers. Then the other integer is x+2.

Both integers are smaller than 10.

Sum of both integers is more than 11.

We conclude and and x is odd integer number.

x can be 5,7.

The two pairs of consecutive odd positive integers are .

** Answer: **

Let x be smaller of two consecutive even positive integers. Then the other integer is x+2.

Both integers are larger than 5.

Sum of both integers is less than 23.

We conclude and and x is even integer number.

x can be 6,8,10.

The pairs of consecutive even positive integers are .

** Answer: **

Let the length of the smallest side be x cm.

Then largest side = 3x cm.

Third side = 3x-2 cm.

Given: The perimeter of the triangle is at least 61 cm.

Minimum length of the shortest side is 9 cm.

** Answer: **

Let x is the length of the shortest board,

then and are the lengths of the second and third piece, respectively.

The man wants to cut three lengths from a single piece of board of length 91cm.

Thus,

if the third piece is to be at least 5cm longer than the second, than

We conclude that and .

Thus , .

Hence, the length of the shortest board is greater than equal to 8 cm and less than equal to 22 cm.

** C lass 11 maths chapter 6 question answer - Exercise: 6.2 **

** Question:1 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot in two half planes.

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

Let there be a point

We observe

i.e. , which is true.

Therefore, half plane (above the line) ** is not a solution ** region of given inequality i.e. ** . **

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

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

This can be represented as follows:

** Question:2 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot in two half-planes.

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

Let there be a point

We observe

i.e. , which is true.

Therefore, half plane II is not a solution region of given inequality i.e.

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

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

This can be represented as follows:

** Question:3 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot into two half-planes.

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

Let there be a point

We observe

i.e. , which is true.

Therefore, the half plane I(above the line) is not a solution region of given inequality i.e. ** . **

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

Thus, the solution to this inequality is half plane II (below the line ) including points on this line, represented by green colour.

This can be represented as follows:

** Question:4 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot in two half-planes.

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

Let there be a point

We observe

i.e. , which is true.

Therefore, half plane II is not solution region of given inequality i.e. ** . **

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:

** Question:5 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot in two half planes.

Let there be a point

We observe

i.e. , which is true.

Therefore, half plane Ii is not solution region of given inequality i.e. ** . **

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:

** Question:6 ** Solve the following inequality graphically in two-dimensional plane: ** **

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot in two half planes.

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

Let there be a point

We observe

i.e. , which is false .

Therefore, half plane I is not solution region of given inequality i.e. ** . **

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:

** Question:7 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot in two half planes.

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

Let there be a point

We observe

i.e. , which is true.

Therefore, half plane II is not solution region of given inequality i.e. ** . **

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:

** Question:8 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in graph below.

The line divides plot in two half planes.

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

Let there be a point

We observe

i.e. , which is true.

Therefore, half plane II is not solution region of given inequality i.e. ** . **

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:

** Question:9 ** Solve the following inequality graphically in two-dimensional plane: ** **

** Answer: **

Graphical representation of is given in graph below.

The line divides plot in two half planes.

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

Let there be a point

We observe

i.e. , which is false.

Therefore, the half plane I is not a solution region of given inequality i.e. ** . **

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:

** Question:10 ** Solve the following inequality graphically in two-dimensional plane:

** Answer: **

Graphical representation of is given in the graph below.

The line divides plot into two half-planes.

Let there be a point

We observe

i.e. , which is true.

Therefore, half plane II is not a solution region of given inequality i.e. ** . **

** 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:

** Class 11 maths chapter 6 question answer - Exercise 6.3 **

** Question:1 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of and is given in the graph below.

The line and divides plot in four regions i.e.I,II,III,IV.

For ,

The solution to this inequality is region II and III including points on this line because points on the line also satisfy the inequality.

For ,

The solution to this inequality is region IV and III including points on this line because points on the line also satisfy the inequality.

Hence, solution to ** is common region of graph i.e. region III. **

** Thus, solution of ** ** is region III. **

This can be represented as follows:

The below green colour represents the solution

** Question:2 ** Solve the following system of inequalities graphically: ** **

** Answer: **

Graphical representation of and is given in graph below.

For ,

The solution to this inequality is region on right hand side of line including points on this line because points on the line also satisfy the inequality.

For ,

The solution to this inequality is region above the line including points on this line because points on the line also satisfy the inequality.

For

The solution to this inequality is region below the line including points on this line because points on the line also satisfy the inequality.

Hence, solution to these linear inequalities is shaded region as shown in figure including points on the respective lines.

This can be represented as follows:

** Question:3 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in the graph below.

For ,

The solution to this inequality is region above line including points on this line because points on the line also satisfy the inequality.

For ,

The solution to this inequality is region below the line including points on this line because points on the line also satisfy the inequality.

Hence, the solution to these linear inequalities is the shaded region(ABC) as shown in figure including points on the respective lines.

This can be represented as follows:

** Question:4 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in the graph below.

For ,

The solution to this inequality is region above line including points on this line because points on the line also satisfy the inequality.

For ,

The solution to this inequality is half plane corresponding to the line containing point excluding points on this line because points on the line does not satisfy the inequality.

Hence, the solution to these linear inequalities is the shaded region as shown in figure including points on line and excluding points on the line .

This can be represented as follows:

** Question:5 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in graph below.

For

The solution to this inequality is region below line excluding points on this line because points on line does not satisfy the inequality.

For ,

The solution to this inequality is region above the line excluding points on this line because points on line does not satisfy the inequality.

Hence, solution to these linear inequalities is shaded region as shown in figure ** excluding points on the lines. **

This can be represented as follows:

** Question:6 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in the graph below.

For

The solution to this inequality is region below line ** in ** cluding points on this line because points on the line also satisfy the inequality.

For ,

The solution to this inequality is region above the line including points on this line because points on the line also satisfy the inequality.

Hence, the solution to these linear inequalities is shaded region as shown in figure including points on the lines.

This can be represented as follows:

** Question:7 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in graph below.

For

The solution to this inequality is region above line including points on this line because points on line also satisfy the inequality.

For ,

The solution to this inequality is region above the line including points on this line because points on line also satisfy the inequality.

Hence, solution to these linear inequalities is shaded region as shown in figure including points on the lines.

This can be represented as follows:

** Question:8 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of and is given in graph below.

For ,

The solution to this inequality is region below line including points on this line because points on line also satisfy the inequality.

For ,

The solution to this inequality represents half plane corresponding to the line containing point excluding points on this line because points on line does not satisfy the inequality.

For ** , **

The solution to this inequality is region on right hand side of the line including points on this line because points on line also satisfy the inequality.

Hence, solution to these linear inequalities is shaded region as shown in figure.

This can be represented as follows:

** Question:9** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in graph below.

For ,

The solution to this inequality is region below the line including points on this line because points on line also satisfy the inequality.

For ,

The solution to this inequality is region right hand side of the line including points on this line because points on line also satisfy the inequality.

For

The solution to this inequality is region above the line including points on this line because points on line also satisfy the inequality.

Hence, solution to these linear inequalities is shaded region as shown in figure including points on the respective lines.

This can be represented as follows:

** Question:10** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in graph below.

For ,

The solution to this inequality is region below the line including points on this line because points on line also satisfy the inequality.

For ,

The solution to this inequality is region below the line including points on this line because points on line also satisfy the inequality.

For

The solution to this inequality is region right hand side of the line including points on this line because points on line also satisfy the inequality.

For

The solution to this inequality is region above the line including points on this line because points on line also satisfy the inequality.

Hence, the solution to these linear inequalities is shaded region as shown in figure including points on the respective lines.

This can be represented as follows:

** Question:11** Solve the following system of inequalities graphically: ** **

** Answer: **

Graphical representation of and is given in graph below.

For ,

For ,

For

Hence, solution to these linear inequalities is shaded region as shown in figure including points on the respective lines.

This can be represented as follows:

** Question:12 ** Solve the following system of inequalities graphically: ** **

** Answer: **

Graphical representation of is given in graph below.

For ,

For ,

For

The solution to this inequality is region right hand side of the line including points on this line because points on line also satisfy the inequality.

For

This can be represented as follows:

** Question:13 ** Solve the following system of inequalities graphically:

** Answer: **

Graphical representation of is given in graph below.

For

The solution to this inequality is region below the line including points on this line because points on the line also satisfy the inequality.

For ,

The solution to this inequality is region above the line including points on this line because points on the line also satisfy the inequality.

For ,

The solution to this inequality is region right hand side of the line including points on this line because points on the line also satisfy the inequality.

For

The solution to this inequality is region right hand side of the line including points on this line because points on the line also satisfy the inequality.

For

This can be represented as follows:

** Question:14 ** Solve the following system of inequality graphically:

** Answer: **

Graphical representation of is given in graph below.

For

For ,

For ,

The solution to this inequality is region left hand side of the line including points on this line because points on the line also satisfy the inequality.

For

The solution to this inequality is region right hand side of the line including points on this line because points on the line also satisfy the inequality.

For

This can be represented as follows:

** Question:15 ** Solve the following system of inequality graphically:

** Answer: **

Graphical representation of is given in graph below.

For

For ,

For ,

For

For

This can be represented as follows:

** Linear inequalities equations ncert solutions - Miscellaneous Exercise **

** Question:1** Solve the inequality

** Answer: **

** Given : **

** Thus, all the real numbers greater than equal to 2 and less than equal to 3 are solutions to this inequality. **

** Solution set is **

** Question:6 ** Solve the inequality

** Answer: **

** Given the linear inequality **

** The solution set of the given inequality is **

** Question:7** Solve the inequality and represent the solution graphically on number line. ** **

** Answer: **

Given :

The solution graphically on the number line is as shown :

** Question:8 ** Solve the inequality and represent the solution graphically on number line.

** Answer: **

Given :

The solution graphically on the number line is as shown :

** Question:9 ** Solve the inequality and represent the solution graphically on number line.

** Answer: **

Given :

The solution graphically on the number line is as shown :

** Question:10 ** Solve the inequality and represent the solution graphically on number line.

** Answer: **

Given :

The solution graphically on the number line is as shown :

** Answer: **

Since the solution is to be kept between 68° F and 77° F.

Putting the value of , we have

the range in temperature in degree Celsius (C) is between 20 to 25.

** Answer: **

Let x litres of 2% boric acid solution is required to be added.

Total mixture = (x+640) litres

The resulting mixture is to be more than 4% but less than 6% boric acid.

and

and

Thus, the number of litres 2% of boric acid solution that is to be added will have to be more than 320 and less than 1280 litres.

** Answer: **

Let x litres of water is required to be added.

Total mixture = (x+1125) litres

It is evident that amount of acid contained in the resulting mixture is 45% of 1125 litres.

The resulting mixture contain more than 25 % but less than 30% acid.

and

and

Thus, the number of litres water that is to be added will have to be more than 562.5 and less than 900 litres.

** Answer: **

Given that group of 12 years old children.

For a group of 12 years old children, CA =12 years

Putting the value of IQ, we obtain

Thus, the range of mental age of the group of 12 years old children is

Definition of Inequality: An inequality is a statement that two values are not equal. In mathematics, inequalities are used to compare values and to represent constraints in real-world problems.

Linear Inequalities: Linear inequalities are a type of inequality where the variables appear only in the first degree, that is, raised to the power of 1.

Solving Linear Inequalities: The process of finding all the possible values of the variable that satisfy a given linear inequality is called solving the inequality. In this chapter, various methods of solving linear inequalities are discussed.

Graphical Representation: Graphical representation is an important tool to visualize the solution of a linear inequality. The chapter 6 class 11 maths discusses how to plot linear inequalities on a coordinate plane.

Solution of System of Linear Inequalities: The NCERT solution for class 11 maths chapter 6 also discusses the solution of a system of linear inequalities, which involves finding the region on the coordinate plane that satisfies all the inequalities in the system.

Application in Real-World Problems: Linear inequalities are widely used in real-world problems, such as optimizing production, minimizing costs, and maximizing profits. The chapter provides various examples of real-world problems that can be solved using linear inequalities.

A manufacturing unit makes two models p and q of a product. Each piece of p requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of q requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The manufacturing unit makes a profit of Rs 8000 on each piece of p and Rs 12000 on each piece of Model q. Formulate this problem in linear equalities to maximize the profit.

The above problem can be formulated using linear inequalities and can be solved using linear programming which you will study in NCERT solutions for class 11 maths chapter 6 linear inequalities.

**The above problem is formulated as follows. **

**Let x is the number of pieces of Model p and y is the number of pieces of Model q **

We have to maximize the profit Z= 8000x+12000y subjected to the following constraints

- NCERT Solutions For Execise 6.1 Class 11 Maths Chapter 6 Linear Inequalities
- NCERT Solutions For Execise 6.2 Class 11 Maths Chapter 6 Linear Inequalities
- NCERT Solutions For Execise 6.3 Class 11 Maths Chapter 6 Linear Inequalities
- NCERT Solutions For Miscellaneous Execise Class 11 Maths Chapter 6 Linear Inequalities

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download EBookchapter-1 | Sets |

chapter-2 | Relations and Functions |

chapter-3 | Trigonometric Functions |

chapter-4 | Principle of Mathematical Induction |

chapter-5 | Complex Numbers and Quadratic equations |

chapter-6 | Linear Inequalities |

chapter-7 | Permutation and Combinations |

chapter-8 | Binomial Theorem |

chapter-9 | Sequences and Series |

chapter-10 | Straight Lines |

chapter-11 | Conic Section |

chapter-12 | Three Dimensional Geometry |

chapter-13 | Limits and Derivatives |

chapter-14 | Mathematical Reasoning |

chapter-15 | Statistics |

chapter-16 | Probability |

**Conceptual Clarity:** The chapter begins by introducing the basic concepts of linear inequalities, ensuring that students understand the fundamental principles.

**Real-Life Applications:** Linear inequalities are explained with reference to real-life scenarios, helping students relate mathematical concepts to practical situations.

**Inequality Notations:** The chapter covers different types of inequality notations, such as "less than," "greater than," "less than or equal to," and "greater than or equal to".

- NCERT solutions for class 11 biology
- NCERT solutions for class 11 maths
- NCERT solutions for class 11 chemistry
- NCERT solutions for Class 11 physics

- Linear inequalities equations ncert solutions will build your fundamentals which will be helpful in solving many real-life problems like maximizing the profit, minimizing the expenditure, allocating the resources with given constraints.
- As all the above class 11 maths ch 6 question answer are prepared and explained in a step-by-step manner with the help of the graphs, it can be understood and visualize the problem easily.
- NCERT solutions for maths chapter 6 class 11 will some innovative ways of solving the problems which become very important to solve some specific problems in an easy way.
- This ch 6 maths class 11 also useful in the prediction of future events based on the past data which is the fundamentals of machine learning

** Happy Reading !!!**

1. What are important topics of the chapter Linear Inequalities ?

Inequalities class 11 includes the important topics such as Basic concept of inequalities, algebraic solutions of linear inequalities in one variable and their graphical representation, graphical solution of linear inequalities in two variables, and solution of system of linear inequalities in two variables. students should practice these concepts to get good a hold of the concepts discussed in class 11 chapter 6.

2. Explain the steps to plot a graph of linear inequality covered in NCERT Solutions for Class 11 Maths Chapter 6.

The steps to plot a graph of a linear inequality covered in linear inequalities class 11 ncert solutions are as follows:

Write the inequality in the form of a linear equation

Solve the equation for y

Identify the boundary line

Choose a test point

Substitute the test point

Shade the region

Identify the solution set

- Label the graph

Students can find NCERT solutions for class 11 maths by clicking on the link.

3. List out the number of exercises present in NCERT solutions for class 11 maths chapter 6.

The linear inequalities class 11 solutions includes there three exercises and one miscellaneous exercise.

Exercise 6.1 – 26 Questions

Exercise 6.2 – 10 Questions

Exercise 6.3 – 15 Questions

Miscellaneous Exercise – 14 Questions

4. Which is the official website of NCERT ?

NCERT official is the official website of the NCERT where you can get NCERT textbooks and syllabus from class 1 to 12.

Oct 15, 2024

Sep 17, 2024

Application Date:09 September,2024 - 14 November,2024

Application Date:09 September,2024 - 14 November,2024

Application Date:01 October,2024 - 30 October,2024

Application Date:01 October,2024 - 30 October,2024

Get answers from students and experts

Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 15th NOV'24! Trusted by 3,500+ universities globally

As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

News and Notifications

Back to top