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NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities

by aglasem
August 26, 2021
in Extras
Reading Time: 1 min read
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NCERT Solutions

NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities – Here are all the NCERT solutions for Class 11 Maths Chapter 6. This solution contains questions, answers, images, explanations of the complete chapter 6 titled Of Linear Inequalities taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook to study Maths, then you must come across chapter 6 Linear Inequalities After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities in one place.

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NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities

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Here on AglaSem Schools, you can access to NCERT Book Solutions in free pdf for Maths for Class 11 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.

For a better understanding of this chapter, you should also see summary of Chapter 6 Linear Inequalities , Maths, Class 11.

Class 11
Subject Maths
Book Mathematics
Chapter Number 6
Chapter Name

Linear Inequalities

NCERT Solutions Class 11 Maths chapter 6 Linear Inequalities

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Class 11, Maths chapter 6, Linear Inequalities solutions are given below in PDF format. You can view them online or download PDF file for future use.

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Question & Answer

Q.1: Solve 24x < 100, when 
(i) x is a natural number.  
(ii) x is an integer.

Ans : The given inequality is 24x < 100. \(\begin{array}{l}{24 x<100} \\ {\Rightarrow \frac{24 x}{24}<\frac{100}{24}} \\ {\Rightarrow x<\frac{25}{6}}\end{array} \quad[\text { Dividing both sides by same positive number] }\) (i) It is evident that 1, 2, 3, and 4 are the only natural numbers less than \(\frac{25}{6}\). Thus, when x is a natural number, the solutions of the given inequality are 1, 2, 3, and 4. Hence, in this case, the solution set is {1, 2, 3, 4}. (ii) The integers less than \(\frac{25}{6}\) are …–3, –2, –1, 0, 1, 2, 3, 4. Thus, when x is an integer, the solutions of the given inequality are …–3, –2, –1, 0, 1, 2, 3, 4. Hence, in this case, the solution set is {…–3, –2, –1, 0, 1, 2, 3, 4}.

Q.2: Solve – 12x > 30, when 
(i) x is a natural number. 
(ii) x is an integer.

Ans : The given inequality is –12x > 30. \(\begin{array}{l}{-12 x >30} \\ {\Rightarrow \frac{-12 x}{-12}<\frac{30}{-12} \quad \quad[\text { Dividing both sides by same negative number }]} \\ {\Rightarrow x <-\frac{5}{2}}\end{array}\) (i) There is no natural number less than \(\left(-\frac{5}{2}\right)\). Thus, when x is a natural number, there is no solution of the given inequality. (ii) The integers less than \(\left(-\frac{5}{2}\right)\) are …, –5, –4, –3. Thus, when x is an integer, the solutions of the given inequality are …, –5, –4, –3. Hence, in this case, the solution set is {…, –5, –4, –3}.

Q.3: Solve 5x – 3 < 7, when 
(i) x is an integer. 
(ii) x is a real number.

Ans : The given inequality is 5x– 3 < 7. \(\begin{array}{l}{5 x-3<7} \\ {\Rightarrow 5 x-3+3<7+3} \\ {\Rightarrow 5 x<10} \\ {\Rightarrow \frac{5 x}{5}<\frac{10}{5}} \\ {\Rightarrow x<2}\end{array}\) (i) The integers less than 2 are …, –4, –3, –2, –1, 0, 1. Thus, when x is an integer, the solutions of the given inequality are …, –4, –3, –2, –1, 0, 1. Hence, in this case, the solution set is {…, –4, –3, –2, –1, 0, 1}. (ii) When x is a real number, the solutions of the given inequality are given by x < 2, that is, all real numbers x which are less than 2. Thus, the solution set of the given inequality is x ∈ (–∞, 2).

Q.4: Solve 3x + 8 >2, when 
(i) x is an integer. (ii) x is a real number.

Ans : The given inequality is 3x + 8 > 2. \(\begin{array}{l}{3 x+8>2} \\ {\Rightarrow 3 x+8-8>2-8} \\ {\Rightarrow 3 x>-6} \\ {\Rightarrow \frac{3 x}{3}>\frac{-6}{3}} \\ {\Rightarrow x>-2}\end{array}\) (i) The integers greater than –2 are –1, 0, 1, 2, … Thus, when x is an integer, the solutions of the given inequality are –1, 0, 1, 2 … Hence, in this case, the solution set is {–1, 0, 1, 2, …}. (ii) When x is a real number, the solutions of the given inequality are all the real numbers, which are greater than –2. Thus, in this case, the solution set is (– 2, ∞).

Q.5: Solve the given inequality for real x: 4x + 3 < 5x + 7

Ans : 4x + 3 < 5x + 7 ⇒ 4x + 3 – 7 < 5x + 7 – 7 ⇒ 4x – 4 < 5x ⇒ 4x – 4 – 4x < 5x – 4x ⇒ –4 < x Thus, all real numbers x,which are greater than –4, are the solutions of the given inequality. Hence, the solution set of the given inequality is (–4, ∞).

NCERT / CBSE Book for Class 11 Maths

You can download the NCERT Book for Class 11 Maths in PDF format for free. Otherwise you can also buy it easily online.

  • Click here for NCERT Book for Class 11 Maths
  • Click here to buy NCERT Book for Class 11 Maths

All NCERT Solutions Class 11

  • NCERT Solutions for Class 11 Accountancy
  • NCERT Solutions for Class 11 Biology
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  • NCERT Solutions for Class 11 Maths
  • NCERT Solutions for Class 11 Economics
  • NCERT Solutions for Class 11 History
  • NCERT Solutions for Class 11 Geography
  • NCERT Solutions for Class 11 Political Science
  • NCERT Solutions for Class 11 Sociology
  • NCERT Solutions for Class 11 Psychology
  • NCERT Solutions for Class 11 English
  • NCERT Solutions for Class 11 Hindi
  • NCERT Solutions for Class 11 Physics
  • NCERT Solutions for Class 11 Business Studies
  • NCERT Solutions for Class 11 Statistics

All NCERT Solutions

You can also check out NCERT Solutions of other classes here. Click on the class number below to go to relevant NCERT Solutions of Class 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Class 1 Class 2 Class 3
Class 4 Class 5 Class 6
Class 7 Class 8 Class 9
Class 10 Class 11 Class 12

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