**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.

## NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities

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

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
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### All NCERT Solutions Class 11

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### All NCERT Solutions

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