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

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

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New post Updated on: 13 Sep 2018, 07:19
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

64% (00:47) correct 36% (00:47) wrong based on 150 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, ∞)

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Originally posted by EgmatQuantExpert on 13 Sep 2018, 02:07.
Last edited by EgmatQuantExpert on 13 Sep 2018, 07:19, edited 2 times in total.
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If |x - 7| > 56, what is the range of x?  [#permalink]

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New post Updated on: 17 Sep 2018, 03:01

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.

Answer: D

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Originally posted by EgmatQuantExpert on 13 Sep 2018, 02:12.
Last edited by EgmatQuantExpert on 17 Sep 2018, 03:01, edited 1 time in total.
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Re: If |x - 7| > 56, what is the range of x?  [#permalink]

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New post 13 Sep 2018, 03:02
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.

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

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New post 13 Sep 2018, 08:13
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.

The best answer is C.


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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New post 13 Sep 2018, 10:28
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.

The best answer is C.


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

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

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New post 14 Sep 2018, 05:57
'D' it is, (-∞, -49) ⋃ (63, ∞)
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Re: If |x - 7| > 56, what is the range of x? &nbs [#permalink] 14 Sep 2018, 05:57
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If |x - 7| > 56, what is the range of x?

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