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RD Sharma Class 11 Maths Solutions Chapter 15 - Linear Inequations

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Last updated date: 17th Jul 2024
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RD Sharma Solutions for Class 11 Maths Chapter 15 - Free PDF Download

In this chapter, the concept of linear inequations in one and two variables is explained. The concept of linear inequations is very helpful in solving problems in science, mathematics, Engineering, Linear programming etc. The solution module provided by Vedantu utilizes various shortcut tips and practical examples to explain all the exercise questions in a simple and easily understandable language. Students who aim to score high marks can refer to RD Sharma Class 11 Solutions Chapter 15 PDF.

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Linear Inequations Solutions- RD Sharma Class 11

Linear Inequations solutions are provided here so that students can study and do well on the main exam. We'll look at linear inequalities in one and two variables in this chapter. Linear inequations are extremely useful in solving issues in science, mathematics, engineering, and linear programming, among other fields. Students who want to get good grades can use the links to download RD Sharma Class 11 Maths Solutions PDF.

The RD Sharma Solutions provide precise answers to the questions in each of the six exercises in Linear Inequations. These RD Sharma Solutions updated for the 2024-25 exam have been developed by Vedantu’s expert teachers in a very straightforward manner that helps students solve issues in the most efficient way possible. Let's take a closer look at the principles covered in this chapter.

An Inequation's Solutions.

  • In one variable, solving linear inequalities.

  • A one-variable solution to a system of linear inequalities.

  • In one variable, there are certain applications of linear inequalities.

  • Graphical solution of linear inequalities in two variables.

  • The solution of two-variable simultaneous linear inequalities.


What is Linear Inequations of RD Sharma Class 11?

When two mathematical assertions or two numbers are compared in a non-equal fashion, inequality develops. Inequalities can be numerical, algebraic, or a combination of the two in nature. Inequalities involving at least one linear algebraic expression, such as when a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, are known as linear inequalities. Linear inequalities can be represented in a number of different ways.

The Symbols Which Represent Inequalities are:

  • < (less than)

  • > (greater than)

  • ≤ (less than or equal to)

  • ≥ (greater than or equal to)

  • ≠ (not equal to)

Strict inequalities are represented by the characters " and '>', while slack inequalities are represented by the symbols " and ". A linear inequality appears to be a linear equation with the inequality sign swapped out for the equality sign.

FAQs on RD Sharma Class 11 Maths Solutions Chapter 15 - Linear Inequations

1. How to solve RD Sharma Class 11 Chapter 15-Linear Inequations?

Solving multi-step one-variable linear inequalities is similar to solving multi-step linear equations: separate the variable from the constants first. According to the laws of inequalities, remember to reverse the inequality sign when multiplying or dividing with negative values while solving multi-step linear inequalities.

  • Step 1: Using the rules of inequality, simplify the inequality on both sides - on the LHS and the RHS.
  • Step 2: If the inequality is a strict inequality, the solution for x is less than or larger than the value obtained as indicated in the question when the value is acquired. If the inequality is not a rigorous inequality, the solution for x is less than, equal to, greater than, or equal to the value obtained in the question.

2. How are linear inequalities used in real life?

A system of linear inequalities is often used to determine the best solution to a problem. It could be as simple as determining how many units of a product should be produced to maximize a profit or as complicated as determining the correct combination of drugs to give a patient.

3. What is the use of linear inequalities?

Linear inequalities are often used to determine the maximum or minimum values of a situation with multiple constraints. For example, it is used to determine how many products should be produced to maximize profit.

4. What is the importance of RD Sharma Solutions for Class 11 Maths Chapter 15 Linear Inequations?

RD Sharma Solutions for Class 11 Maths Chapter 15 Linear Inequations covers all of the major themes in detail, allowing students to better understand the ideas and develop their analytical skills. Students studying for Engineering and other entrance exams should go over Chapter 15 Linear Inequations in RD Sharma Solutions Class 11 Maths. Going over the Class 11 Maths RD Sharma Solutions Chapter 15 will assist you in understanding how to approach and solve the questions.


Expert Vedantu teachers have solved Chapter 15 Linear Inequations. Solutions for Class 11 by RD Sharma Plays a critical part in achieving a high math score for all engineering and other entrance exams. You may obtain RD Sharma Class 11 Maths Chapter 15 Linear Inequations PDF in offline mode by downloading it from the link below.

5. What are important notes of RD Sharma Class 11 Chapter 15- Linear Inequations?

Here's a rundown of some key concepts to remember when studying linear inequalities:

In the case of linear inequalities, there is another relationship between LHS and RHS, such as less than or larger than.

Because the largest power of the variable is 1, a linear inequality is called that.

"Less than" and "greater than" are rigorous linear inequalities, whereas "less than or equal to" and "greater than or equal to" are not.

A hollow dot represents the value produced for x in every linear inequality that employs rigorous linear inequality. It demonstrates that the value obtained is ruled out.

The value found for x is displayed by a solid dot for every linear inequality that is not a rigorous inequality. It demonstrates that the obtained value is included.

6. What are the rules for Linear Inequations of RD Sharma?

Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities. Equivalent inequalities are linear inequalities that have the same solution. For inequalities involving less than or equal to (), and greater than or equal to (), all of the principles listed below apply. Let's take a look at some of the key rules of inequality for all of these operations before learning how to solve linear inequalities.

  • The addition rule of linear inequalities states that adding the same number to each side of the inequality generates an equivalent inequality, meaning the inequality symbol remains the same.

  • Subtraction Rule of Linear Inequalities: The subtraction rule of linear inequalities states that subtracting the same number from either side of the inequality generates an equivalent inequality, meaning that the inequality symbol remains the same.

  • Multiplication Rule of Linear Inequalities: The multiplication rule of linear inequalities states that multiplying both sides of an inequality with a positive number always results in an equivalent inequality, i.e. the inequality symbol does not change.

  • The Division Rule of Linear Inequalities states that dividing both sides of an inequality with a positive number creates an analogous inequality, meaning that the inequality symbol remains unchanged.

7. Where can I find RD Sharma Solutions for Class 11 Maths Chapter 15 Linear Inequation?

Students can find all the solutions of RD Sharma of Class 11 of all the chapters of Maths on our Vedantu website for helping students to get better marks in exams. Solutions help you understand how a formula is used and with practice, you can incorporate that too. Students can download them for free in PDF format. Vedantu also provides additional study materials for all the students which will help them in understanding the formulas and concepts better and will also help them in practicing better. There are live sessions from experts of the subject and doubt clearing sessions for the students who want to clear their doubts and learn better.