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Re: When is |x-4| = 4-x? [#permalink]
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
Re: When is |x-4| = 4-x? [#permalink]
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:
When is |x-4| = 4-x? [#permalink]
09 Dec 2014, 23:29
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.
I am still new to modulus so please do bare with me if I sound stupid.
This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read. So according to the book, I need to take into account when the modulus is positive and negative when solving
\(x-4>0, x>4\)
x-4=4-x x=4 (not sure if this value has to be rejected or not. Please help)
and when \(x+4<0, x<=4\) -(x+4)=4-x -x-4=4-x Just lost here.
My question is why do we chose X<=4 why do we chose one condition over the other.
When is |x-4| = 4-x? [#permalink]
10 Dec 2014, 03:34
Expert's post
saadis87 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.
I am still new to modulus so please do bare with me if I sound stupid.
This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read. So according to the book, I need to take into account when the modulus is positive and negative when solving
\(x-4>0, x>4\)
x-4=4-x x=4 (not sure if this value has to be rejected or not. Please help)
and when \(x+4<0, x<=4\) -(x+4)=4-x -x-4=4-x Just lost here.
My question is why do we chose X<=4 why do we chose one condition over the other.
For the second case, when x - 4 < 0 (x < 4), |x - 4| becomes -(x - 4), so we'd have -(x - 4) = 4 - x, which gives 4 = 4. Since 4 = 4 is true, then it means that for x < -4, |x-4| = 4-x holds true.
Combining x = 4 from the first case and x < 4 from the second, we'll have x <= 4.
Re: When is |x-4| = 4-x? [#permalink]
10 Dec 2014, 04:28
Bunuel wrote:
saadis87 wrote:
I am still new to modulus so please do bare with me if I sound stupid.
This problem can be solved easily by picking numbers but to understand the concepts I tried to solve it using the books I read. So according to the book, I need to take into account when the modulus is positive and negative when solving
\(x-4>0, x>4\)
x-4=4-x x=4 (not sure if this value has to be rejected or not. Please help)
and when \(x+4<0, x<=4\) -(x+4)=4-x -x-4=4-x Just lost here.
My question is why do we chose X<=4 why do we chose one condition over the other.
For the second case, when x + 4 < 0 (x < -4), |x - 4| becomes -(x - 4), so we'd have -(x - 4) = 4 - x, which gives 4 = 4. Since 4 = 4 is true, then it means that for x < -4, |x-4| = 4-x holds true.
Combining x = 4 from the first case and x < -4 from the second, we'll have x <= -4.
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