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

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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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Attachment: Line.PNG [ 7.43 KiB | Viewed 1935 times ]

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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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1225
Location: India
Concentration: International Business, General Management
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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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

Answer = E
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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  B
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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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

(The answer )
Manager  B
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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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

Answer = E

Hi.....E says x+1.....not x-1.....can you clarify please?
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1225
Location: India
Concentration: International Business, General Management
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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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

Answer = E

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

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

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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

Answer = E

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

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

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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

Answer = E

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

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