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Which of the following inequalities is equivalent to -3 < x < 5?

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Which of the following inequalities is equivalent to -3 < x < 5?  [#permalink]

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New post 12 Apr 2017, 05:48
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Which of the following inequalities is equivalent to -3 < x < 5?

A) |x -3| < 5
B) |x -2| < 4
C) |x -1| < 4
D) |x +1| < 4
E) None of the above

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Re: Which of the following inequalities is equivalent to -3 < x < 5?  [#permalink]

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New post 12 Apr 2017, 05:59
amathews wrote:
Which of the following inequalities is equivalent to -3 < x < 5?

A) |x -3| < 5
B) |x -2| < 4
C) |x -1| < 4
D) |x +1| < 4
E) None of the above


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Re: Which of the following inequalities is equivalent to -3 < x < 5?  [#permalink]

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New post 12 Apr 2017, 07:43
amathews wrote:
Which of the following inequalities is equivalent to -3 < x < 5?

A) |x -3| < 5
B) |x -2| < 4
C) |x -1| < 4
D) |x +1| < 4
E) None of the above



Ans C
here's why c is correct
|x -1| < 4
means if |x -1| <0
then -x +1 < 4 ----> -x < 3---->x > -3
also if means if |x -1| >0
then x -1 < 4 ----> x < 5

from above deductions(highlighted)
we have -3 < x < 5

Ans C
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Re: Which of the following inequalities is equivalent to -3 < x < 5?  [#permalink]

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New post 12 Apr 2017, 07:57
The answer should be C, as it is which of the following que. Then its better to start with bottom say ,in opt. D, we can -4 as a value of x, so out now check opt. C, it mataches the range in stem so pick it up ?

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Which of the following inequalities is equivalent to -3 < x < 5?  [#permalink]

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New post 11 Jul 2018, 17:19
Which of the following inequalities is equivalent to -3 < x < 5?

A) |x-3| < 5
B) |x-2| < 4
C) |x-1| < 4
D) |x+1| < 4
E) None of the above.

Solution is C
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Which of the following inequalities is equivalent to -3 < x < 5?  [#permalink]

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New post 11 Jul 2018, 18:01
dawncheadle wrote:
Which of the following inequalities is equivalent to -3 < x < 5?

A) |x-3| < 5
B) |x-2| < 4
C) |x-1| < 4
D) |x+1| < 4
E) None of the above.

Solution is C



Given ,

-3 < x < 5 . Analyzing the given options we have to find the exact range.

This question is designed based on Absolute value. It can be solved as follows:

Option c:

|x-1|<4

case 1 : x-1 is positive .

x-1 <4
x<5

case 2: x-1 is negative .

-(x-1) <4
-x+1 <4
-x <3
x>-3


Combining both cases:

-3<x<5

Thus the best answer is C. In this way we can check other options too.
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Re: Which of the following inequalities is equivalent to -3 < x < 5?  [#permalink]

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New post 22 Jul 2018, 00:04
Answer is C:

|x - 1| < 4

as there is absolute value, we can solve by taking value positively and then negatively:

Positively --> x - 1 < 4 --> x < 5
Negatively --> we flip signs --> -x + 1 < 4 --> -x < 3 --> to make x positive we divide both sides by -1 and get --> x > -3 (inequality sign will flip if we divide by -1)

combining positive and negative --> -3< x < 5 --> same as question, so this is our answer.

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Re: Which of the following inequalities is equivalent to -3 < x < 5? &nbs [#permalink] 22 Jul 2018, 00:04
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