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Which of the following inequalities is equivalent to –2 < x < 4 ?

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Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 05 Nov 2015, 11:17
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Which of the following inequalities is equivalent to –2 < x < 4 ?

(A) | x – 2 | < 4
(B) | x – 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above

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Re: Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 07 Jan 2016, 05:49
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Bunuel wrote:
Which of the following inequalities is equivalent to –2 < x < 4 ?

(A) | x – 2 | < 4
(B) | x – 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above


Instead of verifying each and every option you can figure out this a bit faster in the following manner

|x| < a => -a < x < a . Note that lower limit of x i.e -a and the upper limit of x i.e a essentially sum up to 0

Now if -2 < x < 4, let's say by adding y to this inequality we will get into the above format

-2+y < x+y < 4+y

Now, to move this into the mod format, we need to have (-2+y) + (4+y) = 0 => y = -1

Thus, -3 < x-1 < 3 => |x-1| < 3.

Hence, B
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Re: Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 05 Nov 2015, 12:02
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Bunuel wrote:
Which of the following inequalities is equivalent to –2 < x < 4 ?

(A) | x – 2 | < 4
(B) | x – 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above


(A) | x – 2 | < 4 => -2<x<6: out
(B) | x – 1 | < 3 => –2 < x < 4: yeah
(C) | x + 1 | < 3 => -4<x<2: out
(D) | x + 2 | < 4 => -6<x<2: out
(E) None of the above: out

Ans: B
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Re: Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 07 Jan 2016, 05:20
2
Expand the inequality to remove the absolute value from the expression:

(A) | x – 2 | < 4
Two expressions:
x - 2 < 4 simplifies to x < 6
x - 2 >-4 simplifies to x > -2
Therefore, -2 < x < 6 is not equal to -2 < x < 4 NOT THE ANSWER

(B) | x – 1 | < 3
Two expressions:
x - 1 < 3 simplifies to x < 4
x - 1 > -3 simplifies to x > -2
Therefore, -2 < x < 4 is equal to -2 < x < 4 THIS IS THE ANSWER

(C) | x + 1 | < 3
Two expressions:
x + 1 < 3 simplifies to x < 2
x + 1 > -3 simplifies to x > -4
Therefore, -4 < x < 2 is not equal to -2 < x < 4 NOT THE ANSWER

(D) | x + 2 | < 4
Two expressions:
x + 2 < 4 simplifies to x < 2
x + 2 > -4 simplifies to x > -6
Therefore, -6 < x < 2 is not equal to -2 < x < 4 NOT THE ANSWER

(E) None of the above
Since B is the answer, E cannot be correct
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Re: Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 10 Mar 2016, 10:25
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Re: Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 25 Jul 2016, 04:16
Bunuel wrote:
Which of the following inequalities is equivalent to –2 < x < 4 ?

(A) | x – 2 | < 4
(B) | x – 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above


There is a super easy method to solve such question
First remove the mod
then set the expression to 0
then get a value of X
then add and subtract the value from the given number on the RHS

Lets try with an example (B) --------------> | x – 1 | < 3
First remove the mod -------------------> x-1
then set the expression to 0--------------> x-1=0
then get a value of x---------------------> x=1
then add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2
the range become -2 to 4 correct answer

Now try its with an incorrect option (C) | ----------> |x + 1 | < 3
First remove the mod --------------------------> x+1
then set the expression to 0----------------------> x+1=0
then get a value of x------------------------------> x=-1
then add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4
the range become -4 to 2 Incorrect

THE CORRECT ANSWER IS B
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Re: Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 18 Jun 2017, 01:12
Bunuel wrote:
Which of the following inequalities is equivalent to –2 < x < 4 ?

(A) | x – 2 | < 4
(B) | x – 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above



The best way to do this question would be through number line.

Option b says distance of point x from 1 should be less than 3 which means from 1 you can move to the right till 4 and from 1 you can move left till -2 so that the distance from 1 stays less than 3.
-2<x<4.
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Re: Which of the following inequalities is equivalent to –2 < x < 4 ?  [#permalink]

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New post 23 Aug 2018, 16:10
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Re: Which of the following inequalities is equivalent to –2 < x < 4 ? &nbs [#permalink] 23 Aug 2018, 16:10
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