Problem: If x<0x<0x<0, then ∣x−(x−1)2∣\mid x-\sqrt{(x-1)^{2}} \mid∣x−(x−1)2∣ equals
Answer Choices:
A. 111
B. 1−2x1-2 x1−2x
C. −2x−1-2 x-1−2x−1
D. 1+2x1+2 x1+2x
E. 2x−12 x-12x−1 Solution:
∣x−(x−1)2∣=∣x−∣x−1∣∣=∣x−(1−x)∣=∣−1+2x∣=1−2x\left|x-\sqrt{(x-1)^{2}}\right|=|x-|x-1||=|x-(1-x)|=|-1+2 x|=1-2 x∣∣∣∣x−(x−1)2∣∣∣∣=∣x−∣x−1∣∣=∣x−(1−x)∣=∣−1+2x∣=1−2x.