CAT Practice : Inequalities

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The product of two terms are negative when one of them is negative, and the other positive. If both are negative or positive, the product will be positive. When will these two terms be seperately negative?

Modulus - Quadratic

    Q.8: (|x| - 2) (x + 5) < 0. What is the range of values x can take?

 

  • Correct Answer
    The range is (-∞, -5) or (-2, 2)

Detailed Solution

This can be true in two scenarios.

Scenario I: (|x| - 2) < 0 and (x + 5) > 0
Or |x| < 2 and x > -5.This gives us the range (-2, 2)

Scenario II: (|x| - 2) > 0 and (x + 5) < 0
Or |x| > 2 and x < -5. This gives us the range (-∞, -5)

So, the overall range is (-∞, -5) or (-2, 2)

Correct Answer: (-∞, -5) or (-2, 2)

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Inequalities are crucial to understand many topics that are tested in the CAT. Having a good foundation in this subject will make us tackling questions in Coordinate Geometry, Functions, and most importantly in Algebra much more comfortable.