The question is about Modulus Inequalities. Our task is to identify the range of the given 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 5: Find the range of x where ||x - 3| - 4| > 3?
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, ∞)
The question is "Find the range of x where ||x - 3| - 4| > 3?"
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