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

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Intern
Joined: 24 Jul 2012
Posts: 13
Schools: Schulich '16
GMAT 1: 610 Q49 V26
WE: Consulting (Consulting)
For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

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Updated on: 26 Jul 2012, 07:49
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Difficulty:

55% (hard)

Question Stats:

58% (01:05) correct 42% (01:29) wrong based on 819 sessions

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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

Originally posted by Vamshi8411 on 26 Jul 2012, 05:35.
Last edited by Bunuel on 26 Jul 2012, 07:49, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 47015
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

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26 Jul 2012, 07:56
5
1
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: $$-x=-(-1)=1$$

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]

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26 Jul 2012, 07:42
9
2
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

Regards,
##### General Discussion
Manager
Joined: 26 Jul 2011
Posts: 107
Location: India
WE: Marketing (Manufacturing)
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

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11 Sep 2012, 22:41
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
Intern
Joined: 01 Jun 2012
Posts: 20
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43
GPA: 3.83
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

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09 Oct 2012, 20:19
1
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

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!
Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

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09 Oct 2012, 23:56
1
egiles 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

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.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Joined: 01 Jun 2012
Posts: 20
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43
GPA: 3.83
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

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10 Oct 2012, 09:02
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

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
Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

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10 Oct 2012, 09:55
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

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 $$-(-5)=5.$$
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 13 Aug 2012
Posts: 442
Concentration: Marketing, Finance
GPA: 3.23
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

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06 Dec 2012, 22:37
1
$$\sqrt{-(x + 1)*|x-1| + 1}$$

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)

_________________

Impossible is nothing to God.

Intern
Joined: 02 Nov 2012
Posts: 32
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

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07 Jan 2013, 08:18
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!
Intern
Joined: 20 Dec 2014
Posts: 37
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

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26 Mar 2018, 12:17
Bunuel wrote:
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: $$-x=-(-1)=1$$

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.

Hi

Hypothetically if we land up with a solution as $$\sqrt{- 4}$$ what would be the answer.
Trying to understand the concept.

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Math Expert
Joined: 02 Sep 2009
Posts: 47015
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

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26 Mar 2018, 21:31
MT1988 wrote:
Bunuel wrote:
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: $$-x=-(-1)=1$$

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.

Hi

Hypothetically if we land up with a solution as $$\sqrt{- 4}$$ what would be the answer.
Trying to understand the concept.

It would mean that that you've made an error in arithmetic because even roots, such as square roots from negative numbers are not defined on the GMAT. All numbers in the GMAT are by default real numbers.
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Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?   [#permalink] 26 Mar 2018, 21:31
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