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# If |x/4| > 1 which of the following must be true?

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If |x/4| > 1 which of the following must be true? [#permalink]  16 Apr 2018, 10:00
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If $$|\frac{x}{4}| > 1$$, which of the following must be true?

A. $$x > 4$$

B. $$x < 4$$

C. $$x = 4$$

D. $$x \neq 4$$

E. $$x < - 4$$
[Reveal] Spoiler: OA

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Re: If |x/4| > 1 which of the following must be true? [#permalink]  18 Apr 2018, 01:29
since the inequality involves modulus we should account for both +ve and -ve value

For$$+$$ve value

$$x/4 > 1$$
therefore, $$x>4$$

For $$-$$ve value

$$x/4 < -1$$ (Since this is a inequality multiplying by $$-$$ve number flips the inequality symbol)
$$x < -4$$
The correct option should satisfy both the situation and only choice D does that when x is not equal to $$4$$
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Re: If |x/4| > 1 which of the following must be true?   [#permalink] 18 Apr 2018, 01:29
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