Welcome to ATP Education
ATP Education
6. Linear Inequalities Class 11 mathematics Solutions English Medium-Exercise 6.1
6. Linear Inequalities Class 11 mathematics Solutions English Medium-Exercise 6.1 Get chapter-wise detailed explanations, step-by-step answers, important questions and exam-ready study material in Hindi and English medium.
Topics Covered In This Article
6. Linear Inequalities Class 11 mathematics Solutions English Medium-Exercise 6.1, NCERT Solutions for CBSE Board Classes 6 to 12, ncert solutions for all classes, NCERT SOLUTIONS, online NCERT solutions, NCERT, ncert, ncert solutions, ncert solutions for board exams, ncert Maths solution, Mathematics, ncert science solutions, ncert English book solutions, ncert Hindi book solutions, ncert Social Science book solutions, ncert accounts book solutions, Computer Education, solved question answer for all exercise
6. Linear Inequalities Class 11 mathematics Solutions English Medium-Exercise 6.1
NCERT Solutions for Class 11 are specially prepared according to the latest CBSE syllabus (2026-27) to help students understand every concept clearly. These solutions provide step-by-step explanations, accurate answers, and exam-oriented guidance for all chapters. Class 11 students can improve their problem-solving skills, strengthen conceptual understanding, and prepare confidently for school as well as board examinations. All questions are solved in a simple and easy-to-understand language for both Hindi and English medium learners.
6. Linear Inequalities Class 11 mathematics Solutions English Medium-Exercise 6.1
NCERT Solutions Class 11 mathematics English Medium
6. Linear Inequalities
Topic: Exercise 6.1
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).
All Topics From 6. Linear Inequalities
See other sub-topics of this chapter:
1. Exercise 6.1 2. Exercise 6.2 3. Exercise 6.3 4. Miscellaneous Exercise on Chapter - 6NCERT Solutions Class 11 Hindi and English Medium – Complete Study Material
NCERT Solutions Class 11 students ke liye specially CBSE latest syllabus (2026-27) ke according prepare kiye gaye hain. Yeh solutions Hindi aur English medium dono ke liye available hain, jisse har student apni language preference ke hisaab se padh sakta hai. Har chapter ke sabhi prashnon ke step-by-step answers diye gaye hain jo concept clarity aur exam preparation me madad karte hain.
Chapter-Wise Detailed Explanations
Class 11 ke liye diye gaye Chapter Wise NCERT Solutions me har question ka detailed aur easy explanation diya gaya hai. Chahe aap CBSE Board Exam Preparation kar rahe ho ya school test ke liye revise kar rahe ho, yeh solutions aapko complete understanding denge. Har answer simple language me likha gaya hai jisse students concepts ko easily grasp kar saken.
Hindi and English Medium Support
Students Hindi aur English medium dono me NCERT Book Solutions Class 11 access kar sakte hain. Yeh dual language support un students ke liye helpful hai jo apni regional language me better samajhna chahte hain. Sabhi answers CBSE Latest Syllabus 2026-27 ke anusaar update kiye gaye hain.
Important Features of NCERT Solutions
- Class 11 NCERT Solutions PDF
- CBSE Class 11 Study Material
- NCERT Book Questions and Answers
- Exam Oriented Important Questions
- Step-by-Step Detailed Solutions
- Concept Clarity and Revision Notes
Why Students Should Use NCERT Solutions?
Aaj ke competitive environment me sirf textbook padhna kaafi nahi hota. NCERT Solutions for Class 11 students ko practice aur conceptual understanding dono provide karte hain. Yeh solutions unhe exam pattern samajhne, frequently asked questions practice karne aur high score achieve karne me madad karte hain. Regular practice se students apne weak topics ko improve kar sakte hain.
Best Resource for Exam Preparation
Agar aap Class 11 CBSE Preparation ke liye ek trusted aur reliable source dhundh rahe hain, to yeh NCERT Solutions perfect choice hain. Yeh study material school exams, unit tests, half-yearly aur annual exams ke liye equally useful hai. Har chapter ke answers accurate, verified aur student-friendly format me diye gaye hain.
Isliye agar aap NCERT Solutions Class 11 Hindi and English Medium search kar rahe hain, to yahan aapko complete chapter-wise solutions milenge jo aapki academic journey ko strong aur confident banayenge.