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Chapter Analysis
Intermediate10 pages • EnglishQuick Summary
The chapter 'Linear Inequalities' in the Class 11 NCERT Math textbook introduces the concept of inequalities, explaining how they differ from equations. It covers linear inequalities in one and two variables, discussing both algebraic and graphical methods of solving them. The chapter also includes real-world applications of inequalities and detailed procedures for solving compound inequalities.
Key Topics
- •Definition and examples of linear inequalities
- •Graphical representation of linear inequalities
- •Solving linear inequalities in one variable
- •Solving linear inequalities in two variables
- •Compound inequalities
- •Applications of inequalities in real-world problems
Learning Objectives
- ✓Understand the concept of inequalities and how they differ from equations
- ✓Learn to solve linear inequalities algebraically
- ✓Graphically represent solutions to inequalities on a number line
- ✓Apply inequalities to formulate and solve real-life problems
- ✓Develop procedures for analyzing and solving compound inequalities
Questions in Chapter
Solve 24x < 100, when (i) x is a natural number. (ii) x is an integer.
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Solve – 12x > 30, when (i) x is a natural number. (ii) x is an integer.
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Solve 5x – 3 < 7, when (i) x is an integer. (ii) x is a real number.
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Solve 3x + 8 >2, when (i) x is an integer. (ii) x is a real number.
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Solve the inequalities in Exercises 5 to 16 for real x.
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Additional Practice Questions
Solve the inequality 2x - 5 < 13 and represent it on a number line.
easyAnswer: First, we solve for x: 2x < 18, so x < 9. On a number line, represent this as a circle at 9 with a line extending to the left.
Find the solution set for the inequality 3(x + 2) > x + 10.
mediumAnswer: After expanding and simplifying, 3x + 6 > x + 10 becomes 2x > 4, thus x > 2. The solution set is x ∈ (2, ∞).
A company needs at least 300 units of a product. If each product costs $50 and they cannot spend more than $20,000, how many products can they purchase?
mediumAnswer: The inequality 50x ≤ 20000 gives x ≤ 400. Since they need at least 300, the solution set is 300 ≤ x ≤ 400.
If the cost of manufacturing a product is represented by the inequality 4x + 1500 ≤ 7000, what is the maximum number of products that can be manufactured?
mediumAnswer: Solving 4x ≤ 5500 gives x ≤ 1375. Therefore, the maximum number of products is 1375.
Determine the range of x for which the inequality x^2 - 3x - 4 > 0 holds.
hardAnswer: Factor the quadratic to get (x - 4)(x + 1) > 0. The solution is x < -1 or x > 4.