CAT Practice : Inequalities

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This is an excellent inequality question comprising of both quadratic and modulus!!

Properties of Inequalities

    Q.15:Solve x2 - |x + 3| + x > 0
    1. x
    2. x
    3. x
    4. x

 

  • Correct Answer
    Choice B. x

Detailed Solution

x2 - |x + 3| + x > 0
If x + 3 > 0 x > -3
Then equation is in the form x2 - x - 3+ x > 0 i.e., x2 -3 > 0
x2 > 3 and

But x > -3, thus x >
Now if x + 3 < 0 x < -3
Then equation is in the form x2 + x + 3 + x > 0 x2 + 2x + 3 > 0

Discriminant < 0 a > 0 and iequality > 0 exist for all value of x.
But x < -3 , thus range will be x < -3

Combining both x


Correct Answer: x



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More questions from Inequalities

  1. Inequalities - Integer Solutions
  2. Cubic Inequalities
  3. Quadratic Inequalities
  4. Integer Roots - Trial and Error
  5. Modulus Inequalities
  6. Natural Numbers
  7. Integers - Polynomials
  8. Modulus - Quadratic
  9. Quadratic Inequalities
  10. Inequalities - Integer Solutions
  11. Modulus - Tricky Question
  12. Maximum Possible Value
  13. Inequalities - Integer solutions
  14. Maximum Possible Value
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.