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For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?

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For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink] New post 26 Jul 2012, 04:35
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For x < 0. Simplify \sqrt{-(x + 1)*|x-1| + 1}?

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Jul 2012, 06:49, edited 1 time in total.
Edited the question.
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink] New post 26 Jul 2012, 06:42
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Vamshi8411 wrote:
Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?

A) x

B) x - 1

C) x + 1

D) – x

E) – x + 1

Hi,

for x<0,
|x-1| = 1-x
\sqrt{1-(x + 1) |x-1|}
=\sqrt{1-(x + 1)(1-x)}
=\sqrt{1-1+x^2}
=\sqrt{x^2}
=|x|, again x<0
= -x

Answer (D)

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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink] New post 26 Jul 2012, 06:56
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Expert's post
Vamshi8411 wrote:
For x < 0. Simplify \sqrt{-(x + 1)*|x-1| + 1}?

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1


One can also use plug-in method for this problem.

Since given that x<0, then say x=-1, then \sqrt{-(x + 1)*|x-1| + 1}=\sqrt{-(-1 + 1)*|-1-1| + 1}=\sqrt{0+1}=1.

Now, plug x=-1 into the answer choices to see which one yields 1. Only answer choice D works: -x=-(-1)=1

Answer: D.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink] New post 11 Sep 2012, 21:41
Bunuel/Karishma

How can this be done using algebra. As explained by cyber we have taken value of !X-1! as negative, However we have only been provided with X<0. May be I am missing something..Plz Help
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink] New post 09 Oct 2012, 19:19
cyberjadugar wrote:
Vamshi8411 wrote:
Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?

A) x

B) x - 1

C) x + 1

D) – x

E) – x + 1

Hi,

for x<0,
|x-1| = 1-x
\sqrt{1-(x + 1) |x-1|}
=\sqrt{1-(x + 1)(1-x)}
=\sqrt{1-1+x^2}
=\sqrt{x^2}
=|x|, again x<0
= -x

Answer (D)

Regards,


Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks!
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink] New post 09 Oct 2012, 22:56
1
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egiles wrote:
cyberjadugar wrote:
Vamshi8411 wrote:
Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?

A) x

B) x - 1

C) x + 1

D) – x

E) – x + 1

Hi,

for x<0,
|x-1| = 1-x
\sqrt{1-(x + 1) |x-1|}
=\sqrt{1-(x + 1)(1-x)}
=\sqrt{1-1+x^2}
=\sqrt{x^2}
=|x|, again x<0
= -x

Answer (D)

Regards,


Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks!


What is positive x when x is negative? What do you mean by absolute value of x, when simplified?
Is |-7| = -7? NOOOO! |-7|=-(-7)=7>0!!!
Absolute value is always non-negative.
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink] New post 10 Oct 2012, 08:02
Hi,

for x<0,
|x-1| = 1-x
\sqrt{1-(x + 1) |x-1|}
=\sqrt{1-(x + 1)(1-x)}
=\sqrt{1-1+x^2}
=\sqrt{x^2}
=|x|, again x<0
= -x

Answer (D)

Regards,[/quote]

Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks![/quote]

What is positive x when x is negative? What do you mean by absolute value of x, when simplified?
Is |-7| = -7? NOOOO! |-7|=-(-7)=7>0!!!
Absolute value is always non-negative.[/quote]


Hi EvaJager,

First, many thanks for the help you give me and others on this board. It is much appreciated.

Here is where my answer differed from yours. When I solved it, I reached this point:

= |x|
= x

Here is what you did:

= |x|
= -x

I am confused why you said the absolute value of x is -x. I thought all the absolute value of all numbers is non-negative.

Thanks again!
Eric
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink] New post 10 Oct 2012, 08:55
egiles wrote:
Hi,

for x<0,
|x-1| = 1-x
\sqrt{1-(x + 1) |x-1|}
=\sqrt{1-(x + 1)(1-x)}
=\sqrt{1-1+x^2}
=\sqrt{x^2}
=|x|, again x<0
= -x

Answer (D)

Regards,


Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks![/quote]


--------------------------------
What is positive x when x is negative? What do you mean by absolute value of x, when simplified?
Is |-7| = -7? NOOOO! |-7|=-(-7)=7>0!!!
Absolute value is always non-negative.[/quote]


Hi EvaJager,

First, many thanks for the help you give me and others on this board. It is much appreciated.

Here is where my answer differed from yours. When I solved it, I reached this point:

= |x|
= x

Here is what you did:

= |x|
= -x

I am confused why you said the absolute value of x is -x. I thought all the absolute value of all numbers is non-negative.

Thanks again!
Eric[/quote]

-------------------------
I am asking the same question again: if x = -7, is |-7|=-7??? NO!!!
|-7| = 7. But x is not 7, \,\,x is -7. What is the connection between -7 and 7?
Simply, 7 = -(-7).
When x is negative, multiplying it by -1 it turns it into a positive number. Therefore, |x|=-x for x<0.
You cannot write |-7|=-7. A letter denoting a number if doesn't have a minus sign in front of it, it doesn't mean it cannot be negative. x doesn't automatically designate a positive number. You are stating yourself that x is negative!

Absolute value of a number expresses the distance on the number line between that number and 0. Distance between -7 and 0 is 7.
A number x can be negative, for example x=-7. And -x can be positive, if x=-5, because -(-5)=5.
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink] New post 06 Dec 2012, 21:37
\sqrt{-(x + 1)*|x-1| + 1}

Since x < 0, what is |x+1|?
So let x = -1, x-1 = -2
let x = -2, x-1 = -3
Since x-1 is always (-), |x-1| = -(x-1).

Transform the equation:
\sqrt{-(x+1)*-(x+1)+1}
\sqrt{x^2-1+1}
\sqrt{x^2}=|x|

Since x<0, what is |x|?
|x| = -(x)

Answer: D
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink] New post 07 Jan 2013, 07:18
Can someone please explain why |x-1| = 1-x. I solved the question by filling in -2 and got the answer, but I really want to understand the algebra? Thanks in advance!
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink] New post 13 Apr 2014, 23:04
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?   [#permalink] 13 Apr 2014, 23:04
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