Inequalities 2 | CAT Preparation 2024 | Algebra | Quantitative Aptitude

Introduction

This tutorial is designed to help you understand and solve inequalities, a key topic in algebra that is crucial for CAT (Common Admission Test) preparation. Inequalities often appear in quantitative aptitude sections, and mastering them can significantly boost your chances of achieving a high percentile. This guide will break down the concepts and provide you with practical steps to tackle inequalities effectively.

Step 1: Understand the Basics of Inequalities

• Definition: An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

• Symbols: Familiarize yourself with the common symbols used:

  • Greater than: >
  • Less than: <
  • Greater than or equal to: ≥
  • Less than or equal to: ≤

• Types of Inequalities: There are linear inequalities and non-linear inequalities (like quadratic inequalities). Focus initially on linear inequalities as they are generally more straightforward.

Step 2: Solve Linear Inequalities

• Isolate the Variable: Just like solving equations, the goal is to get the variable on one side.

  • Example: To solve 2x + 5 < 15:
    1. Subtract 5 from both sides: 2x < 10
    2. Divide both sides by 2: x < 5

• Graphing Solutions: Represent the solution on a number line.

  • Use an open circle for less than (<) and greater than (>) and a closed circle for less than or equal to (≤) and greater than or equal to (≥).

Step 3: Solve Compound Inequalities

• Definition: A compound inequality combines two inequalities using 'and' or 'or'.
• Solving Compound Inequalities:
  • For "and" inequalities (e.g., 1 < x < 5):
    • Solve each part separately to find the intersection.
  • For "or" inequalities (e.g., x < 1 or x > 5):
    • Find the union of the two solutions.

Step 4: Practice with Real-World Applications

• Word Problems: Apply inequalities to real-world scenarios, such as budgeting, planning events, or determining limits.

  • Example: If you have a budget of $200 and each item costs $20, the inequality 20x ≤ 200 represents the maximum number of items you can buy.

• Common Pitfalls:

  • Remember to flip the inequality sign when multiplying or dividing both sides by a negative number.
  • Always check your solutions by substituting back into the original inequality.

Step 5: Utilize Online Resources

• Practice Questions: Use platforms like Rodha or other educational websites to find practice problems specifically focused on inequalities.
• Video Tutorials: Watch additional video tutorials that explain complex concepts in different ways, which can help reinforce your understanding.

Conclusion

Mastering inequalities is essential for success in quantitative aptitude, especially for the CAT exam. By understanding the basics, practicing various types of inequalities, and applying them to real-world problems, you can enhance your problem-solving skills. Continue practicing with online resources and consider joining study groups for collaborative learning. Happy studying, and good luck with your CAT preparation!