Problem: x−(y−z)−[(x−y)−z]=x-(y-z)-[(x-y)-z]=x−(y−z)−[(x−y)−z]=
Answer Choices:
A. 2y2y2y
B. 2z2z2z
C. −2y-2y−2y
D. −2z-2z−2z
E. 000
Solution:
[x−(y−z)]−[(x−y)−z]=(x−y+z)−(x−y−z)=x−y+z−x+y+z=2z\begin{aligned} [x-(y-z)]-[(x-y)-z]&=(x-y+z)-(x-y-z) \\ &=x-y+z-x+y+z=2 z \end{aligned} [x−(y−z)]−[(x−y)−z]=(x−y+z)−(x−y−z)=x−y+z−x+y+z=2z