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Which of the following inequalities is an algebraic expression for the

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Princ
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Which of the following inequalities is an algebraic expression for the [#permalink] New post   26 Sep 2018, 06:47
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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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E
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Which of the following inequalities is an algebraic expression for the [#permalink] New post   Updated on: 04 Dec 2018, 03:48
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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

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
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   29 Nov 2018, 02:56
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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 :) )
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   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

Answer = E


Hi.....E says x+1.....not x-1.....can you clarify please?
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   04 Dec 2018, 03:50
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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?
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   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

Answer = E



How do we know which sign to put between x-a and b
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   24 Jan 2019, 05:43
What is X in |X-A| and how does it relate to B?
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   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

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?
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   19 Aug 2019, 05:11
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


Mid point = -1
Distance form either side of midpoint = 3
End points inclusive

|x+1|<=3

IMO E
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   21 Jan 2021, 23:27
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


Does this apply to all questions like this? What if the midpoint is not split evenly?
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   03 Apr 2021, 04:59
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: Which of the following inequalities is an algebraic expression for the [#permalink] New post   19 Oct 2022, 04:07
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Re: Which of the following inequalities is an algebraic expression for the [#permalink]
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