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,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

My page: Ed Prep

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

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.

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.

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!