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# Which of the following inequalities is an algebraic expression for the

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Senior Manager
Joined: 22 Feb 2018
Posts: 428
Which of the following inequalities is an algebraic expression for the  [#permalink]

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26 Sep 2018, 06:47
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Difficulty:

15% (low)

Question Stats:

72% (01:09) correct 28% (00:57) wrong based on 178 sessions

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Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x|≤2
(B) |x|≤4
(C) |x-2|≤2
(D) |x-1|≤3
(E) |x+1|≤3

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Joined: 27 Oct 2017
Posts: 1225
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Which of the following inequalities is an algebraic expression for the  [#permalink]

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Updated on: 04 Dec 2018, 03:48
3
1
This is a very nice question to test the inequality concept

Steps to solve:

1) Plot the midpoint (a) of the solution set on the number line:
here the midpoint, a = (-4+2)/2 = -1

2) Find the distance (b unit) of either end points from the mid point :
here the distance, b = 2-(-1) = -1+4 = 3

3) Insert the appropriate sign of inequality between |x-a| and b:
Here , putting a and b, we get |x-(-1)|≤3

hence, the Required inequality is |x+1|≤3

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Originally posted by gmatbusters on 26 Sep 2018, 08:04.
Last edited by gmatbusters on 04 Dec 2018, 03:48, edited 1 time in total.
Edited a typo
Intern
Joined: 03 Jul 2018
Posts: 9
Location: India
GMAT 1: 610 Q45 V29
Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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29 Nov 2018, 02:56
1
Princ wrote:
Attachment:
Line.PNG

Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x|≤2
(B) |x|≤4
(C) |x-2|≤2
(D) |x-1|≤3
(E) |x+1|≤3

Looking at the number line, we can say that the answer must be -4 ≤ x ≤ 2

Use property : If | x - a | ≤ b then - b ≤ x - a ≤ b

Applying this to option (E), we get the following:

-3 ≤ x+1 ≤3

Solving,

Adding (- 1) on both sides,

=> -3-1 ≤ x +1 -1 ≤ 3-1

=> -4 ≤ x ≤ 2

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Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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04 Dec 2018, 03:20
gmatbusters wrote:
This is a very nice question to test the inequality concept

Steps to solve:

1) Plot the midpoint (a) of the solution set on the number line:
here the midpoint, a = (-4+2)/2 = -1

2) Find the distance (b unit) of either end points from the mid point :
here the distance, b = 2-(-1) = -1+4 = 3

3) Insert the appropriate sign of inequality between |x-a| and b:
Here , putting a and b, we get |x-1|≤3

hence, the Required inequality is |x-1|≤3

Hi.....E says x+1.....not x-1.....can you clarify please?
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Joined: 27 Oct 2017
Posts: 1225
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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04 Dec 2018, 03:50
Thanks for pointing out the typo.
In |x-a|, a= -1 , hence it will be |x+1|.

The above post has been edited.

Thanks

Mansoor50 wrote:
gmatbusters wrote:
This is a very nice question to test the inequality concept

Steps to solve:

1) Plot the midpoint (a) of the solution set on the number line:
here the midpoint, a = (-4+2)/2 = -1

2) Find the distance (b unit) of either end points from the mid point :
here the distance, b = 2-(-1) = -1+4 = 3

3) Insert the appropriate sign of inequality between |x-a| and b:
Here , putting a and b, we get |x-1|≤3

hence, the Required inequality is |x-1|≤3

Hi.....E says x+1.....not x-1.....can you clarify please?

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Joined: 02 Jan 2017
Posts: 46
Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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17 Jan 2019, 05:18
gmatbusters wrote:
This is a very nice question to test the inequality concept

Steps to solve:

1) Plot the midpoint (a) of the solution set on the number line:
here the midpoint, a = (-4+2)/2 = -1

2) Find the distance (b unit) of either end points from the mid point :
here the distance, b = 2-(-1) = -1+4 = 3

3) Insert the appropriate sign of inequality between |x-a| and b:
Here , putting a and b, we get |x-(-1)|≤3

hence, the Required inequality is |x+1|≤3

How do we know which sign to put between x-a and b
Intern
Joined: 15 Sep 2013
Posts: 13
Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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24 Jan 2019, 05:43
What is X in |X-A| and how does it relate to B?
Intern
Joined: 15 Jan 2018
Posts: 41
Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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08 Apr 2019, 10:59
AlN wrote:
gmatbusters wrote:
This is a very nice question to test the inequality concept

Steps to solve:

1) Plot the midpoint (a) of the solution set on the number line:
here the midpoint, a = (-4+2)/2 = -1

2) Find the distance (b unit) of either end points from the mid point :
here the distance, b = 2-(-1) = -1+4 = 3

3) Insert the appropriate sign of inequality between |x-a| and b:
Here , putting a and b, we get |x-(-1)|≤3

hence, the Required inequality is |x+1|≤3

How do we know which sign to put between x-a and b

+1 May I also have some more clarity on this?
Re: Which of the following inequalities is an algebraic expression for the   [#permalink] 08 Apr 2019, 10:59
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