If $x<0$, then $\left|x-\sqrt{(x-1)^2}\right|$ equals
$\textbf{(A) }1\qquad \textbf{(B) }1-2x\qquad \textbf{(C) }-2x-1\qquad \textbf{(D) }1+2x\qquad  \textbf{(E) }2x-1$
We have $\sqrt{x^2} = |x|$, so we rewrite the expression as follows.
\[|x - \sqrt{(x-1)^2}| = |x - |x-1||\]
We know that $x < 0$, so $x-1 < 0$. Thus, we can rewrite $|x-1|$ as $1-x$. So
\[|x - |x-1|| = |x - (1-x)| = |2x - 1|\].
Since $x< 0, 2x-1 < 0$. Thus, we can write this as
\[|2x - 1| = 1- 2x\]
$\boxed{B}$

~JustinLee2017