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amathews
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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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dawncheadle
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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Hi Bunuel
Instead of plugging each option isn't there a faster way to do this?
#1.Find half of range 5-(-3) =8/2 =4.
This leaves us with options B, C, D.
#2. Find the half mean 5+(-3)=2/2 =1
So |x-1|<4
OPTION C

Does this work everytime?

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