CAT Practice : Inequalities

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Similar to a previous question. When will the equation have an odd number of negative terms? When will it have an even number?

Inequalities - Integer Solutions

    Q.5: Find the range of x where ||x - 3| - 4| > 3. < 0?

 

  • Correct Answer
    ( -∞, -4) or (2, 4) or ( 10, ∞)

Detailed Solution


If we have an inequality |y| > 3, this will be satisfied if => y > 3 or y < -3.

So, the above inequality simplifies to two inequalities

Inequality I: |x - 3| - 4 > 3
|x - 3| - 4 > 3 => |x - 3| > 7
x - 3 > 7 or x - 3 < -7
Or, x > 10 or x < -4

Of, x lies outside of -4 and 10. Or, x can lie in the range (-∞, -4) or ( 10, ∞)

Inequality II: |x - 3| - 4 < -3
|x - 3| - 4 < - 3
=> |x - 3| < 1
=> -1 < x - 3 < 1 or x lies between 2 and 4

So, final solution is given by the range
( -∞, -4) or (2, 4) or ( 10, ∞)

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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.