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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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