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# If |x - 7| > 56, what is the range of x?

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Joined: 04 Jan 2015
Posts: 2892
If |x - 7| > 56, what is the range of x?  [#permalink]

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Updated on: 13 Sep 2018, 08:19
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Difficulty:

25% (medium)

Question Stats:

67% (01:04) correct 33% (01:02) wrong based on 233 sessions

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Different methods to solve absolute value equations and inequalities- Exercise Question #4

If |x - 7| > 56, what is the range of x?

Options

a) (-56, 56)
b) (-63, 63)
c) (-49, 63)
d) (-∞, -49) ⋃ (63, ∞)
e) (-∞, -56) ⋃ (56, ∞)

To read the article: Different methods to solve absolute value equations and inequalities

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Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:07.
Last edited by EgmatQuantExpert on 13 Sep 2018, 08:19, edited 2 times in total.
e-GMAT Representative
Joined: 04 Jan 2015
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If |x - 7| > 56, what is the range of x?  [#permalink]

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Updated on: 17 Sep 2018, 04:01

Solution

Given:
• We are given an absolute value inequality, |x - 7| > 56
• Note that we do not have any constraint on x. So, x can be an integer or a decimal

To find:
• We need to find the range of values of x, that satisfies the given inequality

Approach and Working:
• We know that, the range of x, for |x| > a, is x < -a ⋃ x > a
• So, the range of x, for |x - 7| > 56, is
o x – 7 < -56 ⋃ x - 7 > 56
o Implies, x < -49 ⋃ x > 63
• Therefore, the range of values of x, that satisfies the inequality, |x - 7| > 56, is (-∞, -49) ⋃ (63, ∞)

Hence, the correct answer is option D.

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Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:12.
Last edited by EgmatQuantExpert on 17 Sep 2018, 04:01, edited 1 time in total.
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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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Re: If |x - 7| > 56, what is the range of x?  [#permalink]

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13 Sep 2018, 04:02
Since this question is designed based on absolute value , we have to asses both negative and positive aspects of x.

1. when x is positive:

x - 7> 49

x > 63

2. when x is negative :

- x + 7 > 56

x< -49.

So, -49<x<63.

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Re: If |x - 7| > 56, what is the range of x?  [#permalink]

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13 Sep 2018, 09:13
selim wrote:
Since this question is designed based on absolute value , we have to asses both negative and positive aspects of x.

1. when x is positive:

x - 7> 49

x > 63

2. when x is negative :

- x + 7 > 56

x< -49.

So, -49<x<63.

Shouldn't it be x<-49 and x>63? So D is the answer
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Re: If |x - 7| > 56, what is the range of x?  [#permalink]

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13 Sep 2018, 11:28
selim wrote:
Since this question is designed based on absolute value , we have to asses both negative and positive aspects of x.

1. when x is positive:

x - 7> 49

x > 63

2. when x is negative :

- x + 7 > 56

x< -49.

So, -49<x<63.

Because the inequality sign point to the right we know that the answer will be in the "or" form, hence A, B and C are out.
Now solve for the two cases :
x-7>56 --> x>63
x-7<-56 (do not forget to switch the sign for the negative case) --> x<-49

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Re: If |x - 7| > 56, what is the range of x?  [#permalink]

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14 Sep 2018, 06:57
'D' it is, (-∞, -49) ⋃ (63, ∞)
Re: If |x - 7| > 56, what is the range of x?   [#permalink] 14 Sep 2018, 06:57
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