NCERT Solutions for Class 11 – Complete Chapter-wise Study Material
6. Linear Inequalities is one of the most important chapters in the Class 11 Mathematics English NCERT Solutions curriculum. This chapter plays a significant role in helping students build a strong conceptual foundation while preparing for school examinations, class tests, unit tests, half-yearly examinations, annual examinations, and CBSE board assessments. The chapter has been carefully designed according to the latest NCERT syllabus, making it an essential part of every student's study plan.
The 6. Linear Inequalities - Class 11 Mathematics English NCERT Solutions available on ATP Education explain every question in a simple, accurate, and step-by-step manner. Each answer is prepared according to the latest CBSE guidelines so that students can understand the concepts clearly without confusion. Whether you are completing your homework, revising before examinations, or strengthening your understanding of the subject, these solutions provide reliable academic support throughout your learning journey.
One of the biggest advantages of studying 6. Linear Inequalities is that it helps students understand important concepts, definitions, examples, and textbook exercises in an organized way. Instead of memorizing answers, students learn how to develop logical thinking, improve analytical skills, and write well-structured answers in examinations. This chapter also helps improve problem-solving ability and encourages conceptual learning, which is essential for scoring higher marks in school and competitive examinations.
Our Class 11 Mathematics NCERT Solutions cover all textbook questions, important exercise questions, and chapter-wise explanations in English Medium. Every solution is written in easy-to-understand language, allowing students to revise the chapter quickly before examinations. Regular practice of these solutions improves confidence, strengthens subject knowledge, and reduces examination stress.
Students preparing for school assessments should carefully study 6. Linear Inequalities because questions from this chapter are frequently asked in objective questions, short answer questions, long answer questions, competency-based questions, and case-study questions. Understanding the concepts explained in this chapter also helps students connect related topics from other chapters, making overall learning more effective and meaningful.
At ATP Education, we continuously update our Class 11 Mathematics English NCERT Solutions according to the latest NCERT textbooks and CBSE curriculum. Students can confidently use these chapter-wise solutions for daily study, homework assistance, quick revision, examination preparation, and self-learning. By studying 6. Linear Inequalities thoroughly and practising every question regularly, students can strengthen their concepts, improve writing skills, and achieve better academic performance in both school and board examinations.
6. Linear Inequalities - Class 11 Mathematics English NCERT Solutions
6. Linear Inequalities
Exercise 6.1
Q1. Solve 24x < 100, when
(i) x is a natural number
(ii) x is an integer
Solution:
The given inequality is 24x < 100.
(i) It is evident that 1, 2, 3, and 4 are the only natural numbers less than
∴ 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}.
(i) It is evident that 1, 2, 3, and 4 are the only natural numbers less than
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}.
Q2. Solve –12x > 30, when
(i) x is a natural number
(ii) x is an integer
Solution:
The given inequality is –12x > 30.
(i) There is no natural number less than
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}.
Q3. Solve 5x– 3 < 7, when
(i) x is an integer
(ii) x is a real number
Soluution:
The given inequality is 5x– 3 < 7.
Q5. Solve the given inequality for real x: 4x + 3 < 5x + 7
Solution :
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, ∞).
Q23. Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
Solution:
Let x be the smaller of the two consecutive odd positive integers.
Then, the other integer is x + 2.
Since both the integers are smaller than 10, x + 2 < 10
⇒ x < 10 – 2
⇒ x < 8 … (1)
Also, the sum of the two integers is more than 11.
∴x + (x + 2) > 11
⇒ 2x + 2 > 11
⇒ 2x > 11 – 2
⇒ 2x > 9
⇒ x > 9/2
⇒ x > 4.5 ....... (2)
From (1) and (2), we get .
Since x is an odd number, x can take the values, 5 and 7.
Therefore, the required possible pairs are (5, 7) and (7, 9).
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NCERT Book Solutions
Chapter-wise NCERT Solutions for Class 6 to 12 prepared according to the latest CBSE syllabus.
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NCERT Solutions Class 11
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NCERT Book Solutions
Chapter-wise NCERT Solutions for Class 6 to 12 prepared according to the latest CBSE syllabus.
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Studying from NCERT Solutions helps students build strong conceptual understanding and improve problem-solving skills. These solutions are especially useful for revision because every answer is written according to the marking scheme followed by CBSE.
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All NCERT Book Solutions for Class 11 available on ATP Education are updated according to the latest CBSE curriculum. Whenever NCERT introduces changes in textbooks or syllabus, our study materials are revised accordingly so that students always receive accurate and updated content.
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NCERT textbooks form the foundation of many competitive examinations. Students preparing for Olympiads, NTSE, CUET, UPSC Foundation, SSC and several entrance examinations can strengthen their basics through these chapter-wise solutions. Understanding NCERT concepts also improves analytical thinking and logical reasoning.
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