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 \(-(-5)=5.\)

_________________

PhD in Applied Mathematics

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