Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 11 Mathematics 6. Linear Inequalities to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 11 Mathematics 6. Linear Inequalities to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 6.1. Whether you are studying for board exams or mid-term exams, 11 Mathematics Chapter 6. Linear Inequalities solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsExercise 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).
Exercise 6.1 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 11 Mathematics Chapter 6. Linear Inequalities solutions help you understand the core concepts and practice effectively.
Revision is the key to exam success. Our notes for 11 Mathematics highlight important formulas, key definitions, and exam-ready points from Chapter 6. Linear Inequalities. These quick revision notes make last-minute preparation easy.
Every NCERT chapter ends with exercises, and solving them is crucial. Our Exercise 6.1 include complete solutions for 11 Mathematics Chapter 6. Linear Inequalities exercises. With step-by-step answers, you gain clarity and confidence to attempt similar exam questions.
To boost your preparation, we also provide additional important questions with answers. These are prepared from previous year board papers, sample papers, and important concepts of Chapter 6. Linear Inequalities. Practicing these ensures you are well-prepared for both board and mid-term exams.
Our Exercise 6.1 are useful for both board exams and mid-term exams. For 11 Mathematics, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 6.1 for 11 Mathematics Chapter 6. Linear Inequalities are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
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