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When is |x-4| = 4-x?

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Re: When is |x-4| = 4-x? [#permalink] New post 19 Dec 2013, 05:54
Silly me, thats correct
Thanks
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J:)

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Re: When is |x-4| = 4-x? [#permalink] New post 21 Jan 2014, 23:30
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|={-(some \ expression)}. For example: |-5|=5=-(-5);

When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|={some \ expression}. For example: |5|=5;

So, |x-4|=4-x=-(x-4) to be true should be that x-4\leq{0} --> x\leq{4}.

Answer: D.

Hope it's clear.


This might sound silly but i just started preparing for GMAT, and I have a question. Why is it then in some cases we take x<0 or x>0 and in this problem we have x<=0 and x>=0

Thank you.
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Re: When is |x-4| = 4-x? [#permalink] New post 23 Jan 2014, 02:50
Expert's post
bytatia wrote:
Bunuel wrote:
nkimidi7y wrote:
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0

I could answer this question by plugging in some numbers.
But how do i prove this using algebra?


Absolute value properties:

When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|={-(some \ expression)}. For example: |-5|=5=-(-5);

When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|={some \ expression}. For example: |5|=5;

So, |x-4|=4-x=-(x-4) to be true should be that x-4\leq{0} --> x\leq{4}.

Answer: D.

Hope it's clear.


This might sound silly but i just started preparing for GMAT, and I have a question. Why is it then in some cases we take x<0 or x>0 and in this problem we have x<=0 and x>=0

Thank you.


Well, it all depends on the problem at hand. For this problem, we need = sign because x=4 also satisfies |x-4| = 4-x.

Below posts might help to brush up fundamentals on modulus:
Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

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Re: When is |x-4| = 4-x? [#permalink] New post 24 Jan 2014, 00:03
When is |x-4| = 4-x?

A. x=4
B. x=0
C. x>4
D. x<=4
E. x< 0


|x-4| = 4-x

Or, \frac{|x-4|}{x-4}=-1

=> (x-4) < 0 or x = 0

Or, x <= 4

Answer: (D)
Re: When is |x-4| = 4-x?   [#permalink] 24 Jan 2014, 00:03
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