Class 11 Maths
Linear Inequalities
Solution for linear inequality in one variable
Solution & Solution Set
Solution: Values of x, which make inequality a true statement. E.g. 3 is a solution for x<7
Solution Set: The set of values of x is called its solution set. E.g.: 1,2,3,4,5,6 is solution set for x<7 where x is natural Number
Rules of Inequality:
- Equal numbers may be added to (or subtracted from) both sides of an inequality without affecting the sign of inequality. E.g. x<7 is same as x +2 <7+ 2
- Both sides of an inequality can be multiplied (or divided) by the same positive number without affecting the sign of inequality. E.g. : x+y <7 is same as (x+y) *3 < 7 * 3
- But when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed g. : x+y <7 is same as (x+y) *(-3) > 7 *(- 3)
Numerical: Solve 30 x < 160 when (i) x is a natural number, (ii) x is an integer, (iii) x is real number
Solution: Dividing the inequality by 30 as per rule 2.
30/30 x < 160/30
Or x< 16/3
Case 1: X is a natural number. Then solution set is {1,2,3,4,5}
Case 2: X is an integer. Then solution set is {……-4,-3,-32,-1,0,1,2,3,4,5}
Case 3: X is a real number. Then solution set is (–∞,16/3).
We can represent case 3 solution using number line
Numerical: Solve 7x + 2 ≤ 5x + 8. Show the graph of the solutions on number line.
Solution: Subtracting 2 from both side we get
7x ≤ 5x + 6
Subtracting 5x from both side we get
2x ≤ 6
Dividing 2 both side we get
x ≤ 3
We can represent this in Number line below.
Class 11 Maths Linear Inequalities NCERT Chapter 5 Free Notes for Best Revision
Revision of Class 11 Maths Linear Inequalities is a crucial aspect of effective learning. Revision plays a vital role in the learning process and is especially important before exams. Here are some key points you can consider emphasizing in your content:
- Retention and Memory: Regularly reviewing and revisiting the material of Class 11 Maths Linear Inequalities helps reinforce the concepts in students' minds. It strengthens memory pathways, making it easier to recall information during exams and beyond.
- Consolidation of Knowledge: When you revise notes, you are essentially consolidating your knowledge. This means connecting new information with what you already know, making the overall understanding more robust.
- Identifying Knowledge Gaps: Revision allows students to identify any gaps in their understanding or areas where they need further clarification. This gives you a chance to seek help or delve deeper into those topics. For detailed understanding, you can always refer to the videos of Linear Inequalities Class 11 Maths NCERT Chapter 5 on LearnoHub.com
- Building Confidence: As you revise Linear Inequalities Class 11 Maths and become more familiar with the content, your confidence in your abilities grows. Confidence is a crucial factor in exam performance as it reduces anxiety and allows you to approach exams with a positive mindset.
- Different Revision Techniques: Use a variety of revision techniques such as summarizing notes, creating flashcards, practicing past papers, discussing concepts with peers, and teaching others. Different techniques work for different students, and it's essential to find what suits you the best. You can also attend the LIVE Revision classes on LearnoHub.com or watch the LIVE Revision Race videos of LearnoHub on Linear Inequalities Class 11 Maths NCERT Chapter 5.
- Spacing Effect: Spacing out revision sessions over time, rather than cramming all at once, has been shown to improve long-term retention. Create a revision schedule leading up to the exams to allow for spaced practice.
- Regular Revision over Cramming: Regular and consistent revision throughout the academic year is very important. Waiting until the last moment to cram everything can be overwhelming and less effective than spaced-out revision.
- Self-Assessment: Assess your understanding periodically through quizzes or self-tests. This helps you to gauge your progress and identify areas that need further attention. Refer Class 11 Linear Inequalities Online Tests.
- Balanced Approach: Remind students to strike a balance between revision and other activities. Adequate rest, exercise, and relaxation are essential for optimal learning and performance.
- Seeking Help: If you face difficulties during the revision process, Refer the videos of Class 11 Maths Linear Inequalities. Clearing doubts promptly is crucial for a better grasp of the subject matter. You can always ask your doubts on Linear Inequalities Class 11 Maths NCERT Chapter 5. “Ask a Question” section of LearnoHub.com
By highlighting the benefits and strategies of effective revision, you can approach your studies more mindfully and achieve better results in your exams. Best of luck bachhon!
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Always remember, it is very important to study with full concentration during Revision. Here are a few tips for you on how to revise with full focus:
- Create a Distraction-Free Environment: Find a quiet and comfortable place to study where you can minimize distractions. Turn off or silence your phone, log out of social media accounts, and inform others around you that you need uninterrupted study time. A dedicated study environment will help you focus better.
- Set Specific Goals: Before starting your study session, set clear and achievable goals. Break down your study material into smaller tasks, and plan what you want to accomplish during each session. Having specific goals will give you a sense of direction and purpose, making it easier to concentrate.
- Use the Pomodoro Technique: The Pomodoro Technique is a time management method that involves studying in short, focused intervals, typically 25 minutes, followed by a short break of 5 minutes. After completing four sessions, take a longer break of around 15-30 minutes. This technique can improve focus and productivity by providing regular breaks to recharge.
- Stay Organized: Keep your study materials, notes, and resources well-organized. Having everything you need at hand will save time and reduce distractions caused by searching for materials. Use color-coded folders or digital tools to maintain a structured study system.
- Practice Mindfulness and Meditation: Before you begin studying, take a few minutes to practice mindfulness or meditation. Deep breathing exercises and clearing your mind of distractions can help you approach your study session with a calm and focused mindset.
Remember, studying with full concentration is a skill that takes time and practice to develop. If you find your mind wandering during study sessions, gently bring your focus back to the task at hand and be patient with yourself. With consistent effort, you can improve your ability to concentrate and make the most of your study time.
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