How does (1-x)-1 equal (x-2)

Here are my issues.
1. Can I arrange the equation -1(1-x)? If not why not? I am confused by some algebra rules here.

2. How can I just switch the (1-x) to (x-1). In (1-x) the 1 is positive, and in (x-1) its negative???

3. How do I just subtract the -1 from whats inside the parens? Don't I get (1-x-1)? Is this equal to (2-x)?

Question

How does (1-x)-1 equal (x-2)

Here are my issues. 
1. Can I arrange the equation -1(1-x)? If not why not? I am confused by some algebra rules here.

2. How can I just switch  the (1-x) to (x-1). In (1-x) the 1 is positive, and in (x-1) its negative???

3. How do I just subtract the -1 from whats inside the parens? Don't I get (1-x-1)? Is this equal to (2-x)?

anonymous · Answer

in general it doesn't

anonymous · Answer

Can you  number your answer so I know which question you are addressing? 
(Even though they are all related haha)

anonymous · Answer

i am assuming by ! you do not mean factorial. 
$1-x-1=-x$ and
 $-x=x-2\iff -2x=-2\iff x=2$

anonymous · Answer

Yes lol let me fix that

anonymous · Answer

it is not clear to me what the question is
if it is "solve for $x$: $1-x-1=x-2$ then the answer is $x=2$

anonymous · Answer

oh Im taking the derivative, but Im just simplifiying here

anonymous · Answer

Im taking the derivative of (1-x)e^-x  and one of the parts I am simplifying is (1-x)-1 
And I don't get exactly how and why (1-x)-1 equals (x-2)