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Inequalities - 3 Video Lecture | Quantitative Aptitude (Quant) - CAT

FAQs on Inequalities - 3 Video Lecture - Quantitative Aptitude (Quant) - CAT

1. What are linear inequalities and how do they differ from linear equations?

Ans. Linear inequalities are mathematical expressions that show the relationship between two expressions using inequality symbols (such as <, >, ≤, or ≥). Unlike linear equations, which assert that two expressions are equal, linear inequalities indicate that one expression is greater than or less than another, allowing for a range of solutions rather than a single point.

2. How do you graph linear inequalities on a coordinate plane?

Ans. To graph a linear inequality, first graph the corresponding linear equation as if it were an equality. Use a solid line for inequalities that include equality (≤ or ≥) and a dashed line for strict inequalities (< or >). Then, choose a test point (often the origin) to determine which side of the line to shade, indicating the set of solutions that satisfy the inequality.

3. Can you explain how to solve a system of linear inequalities?

Ans. To solve a system of linear inequalities, first, graph each inequality on the same coordinate plane. The solution to the system is the region where the shaded areas of all inequalities overlap, representing all the points that satisfy all the inequalities simultaneously.

4. What are some real-world applications of linear inequalities?

Ans. Linear inequalities are used in various real-world scenarios, such as budgeting (where expenses must not exceed income), resource allocation (ensuring limits on materials or time), and optimization problems (like maximizing profit or minimizing costs while staying within constraints).

5. How can I check if a particular point is a solution to a linear inequality?

Ans. To check if a point is a solution to a linear inequality, substitute the coordinates of the point into the inequality. If the resulting statement is true, then the point is a solution. If it is false, the point does not satisfy the inequality.

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Oct 15, 2025 Last updated

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167 videos|229 docs|95 tests

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