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Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of

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Russ19
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Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of [#permalink] New post   08 Feb 2020, 10:09
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Given x<1, the expression \(\sqrt{(x-1)^2} +x\) is equivalent to which of the following choices?

(A) -1

(B) 1

(C) 2x - 1

(D) 1 - 2x

(E) 2x + 1
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B
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shameekv1989
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Re: Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of [#permalink] New post   08 Feb 2020, 10:47
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\(\sqrt{(x-1)^2}\) = |x-1|

|x-1| = -x+1 when x<1

Therefore -x+1+x = 1 -> Answer - B
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Re: Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of [#permalink] New post   09 Feb 2020, 14:07
shameekv1989 how did you derive the equation to solve this problem?
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Re: Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of [#permalink] New post   09 Feb 2020, 14:19
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ahengartner wrote:
shameekv1989 how did you derive the equation to solve this problem?


ahengartner :- Which equation are you talking about?

\(\sqrt{(x-1)^2}\) -> When you take a square root of a variable (a perfect square) it will be an absolute value, in this cae, |x-1|

So when you open an absolute there are 2 possiblities i.e. \(x-1<0\) -> \(x<1\) and \(x-1>0\) -> \(x>1\).

And it is given in the question that x<1. So we consider only when x<1 i.e. x-1 < 0.

We write an absolute as negative when it is <0 when we open i.e. |x-1| = -(x-1) when (x-1) < 0 i.e. when x<1.
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Re: Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of [#permalink] New post   11 Sep 2023, 22:06
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shameekv1989 wrote:
\(\sqrt{(x-1)^2}\) = |x-1|

|x-1| = -x+1 when x<1

Therefore -x+1+x = 1 -> Answer - B


Hi,

How did you go from |x-1| = -x+1 to -x+1+x= 1 ?
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Re: Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of [#permalink]
11 Sep 2023, 22:06
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