The question is about an inequality that contains modulus. Our task is to find out the range of the x in the inequality. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.
Question 8: (|x| - 2) (x + 5) < 0. What is the range of values x can take?
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)
The question is "(|x| - 2) (x + 5) < 0. What is the range of values x can take?"
CAT® (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.
2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093