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# Which of the following equations forms the solution set for all real n

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Senior Manager
Joined: 15 Oct 2015
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Concentration: Finance, Strategy
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Which of the following equations forms the solution set for all real n [#permalink]

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16 Feb 2016, 02:43
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Which of the following equations forms the solution set for all real numbers that are 6 units away from -4?

$$|{x + 4}| = 6$$

$$|{x - 4}| = 6$$

$$|{x + 6}| = 4$$

$$|{x - 6}| = 4$$

$$|{x + 6}| = -4$$
[Reveal] Spoiler: OA
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Posts: 44566
Re: Which of the following equations forms the solution set for all real n [#permalink]

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16 Feb 2016, 03:02
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Nez wrote:
Which of the following equations forms the solution set for all real numbers that are 6 units away from -4?

$$|{x + 4}| = 6$$

$$|{x - 4}| = 6$$

$$|{x + 6}| = 4$$

$$|{x - 6}| = 4$$

$$|{x + 6}| = -4$$

6 units away from -4 are two numbers -4 + 6 = 2 and -4 - 6 = -10.

Both, 2 and -10, are the roots of only the first equation:

$$|{x + 4}| = 6$$ --> $$x + 4= 6$$, so $$x = 2$$ or $$x + 4= -6$$, so $$x = -10$$.

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Re: Which of the following equations forms the solution set for all real n [#permalink]

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22 Aug 2016, 20:45
Nezdem wrote:
Which of the following equations forms the solution set for all real numbers that are 6 units away from -4?

$$|{x + 4}| = 6$$

$$|{x - 4}| = 6$$

$$|{x + 6}| = 4$$

$$|{x - 6}| = 4$$

$$|{x + 6}| = -4$$

From the Statement : set for all real numbers that are 6 units away from -4 : x > 6-4 and < -6-4

-10 > x > 2
add 4 on both sides of the equation
= -6 > x+4 > 6 which is same as |x + 4| <6 answer is A)

+1 for kudos
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Re: Which of the following equations forms the solution set for all real n [#permalink]

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30 Mar 2018, 14:41
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following equations forms the solution set for all real n   [#permalink] 30 Mar 2018, 14:41
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