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If |x| / |3| > 1, which of the following must be true?

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Joined: 20 Aug 2015
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Re: If |x| / |3| > 1, which of the following must be true? [#permalink]  22 Sep 2015, 01:28
Expert's post
Himalayan wrote:
If |x|/|3| > 1, which of the following must be true?

A. x > 3
B. x < 3
C. x = 3
D. x ≠ 3
E. x < -3

Modulus of a number always tells us the absolute value or put simply the positive value of a number.
Modulus of a positive number will always be the same number
Modulus of a negative number will be just the positive part of the number

In this question, 3 is a positive number, hence |3| = 3
Hence we have $$|x|/3 > 1$$

or |x| > 3.
This means x > 3 or x <-3

Of the given options, the only option that does not hold good is Option D

Solving modulus inequality
If |x| > a, then the inequality will pan out as x > a and x< -a
If |x| < a, then the inequality will pan out as -a < x <a

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Re: If |x| / |3| > 1, which of the following must be true?   [#permalink] 22 Sep 2015, 01:28

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