IS |x-z|=|z-y|?

[royaamir]

Date efficiency.....

Is |x-z|=|z-y|????
1. x=y
2.|x|-z=|y|-z

I am confused why the answer is A.
Please help!!!
Thanks...

[RonPurewal]

Date efficiency.....

Is |x-z|=|z-y|????
1. x=y
2.|x|-z=|y|-z

I am confused why the answer is A.
Please help!!!
Thanks...

i'll show you how to work with statement (1), since you haven't really requested any help with the other statement.

first approach: ALGEBRA
since x and y are equal, you can substitute x for y, giving
Is |x - z| = |z - x|?
the answer to this question is definitely yes, since the quantities x - z and z - x are opposites, and the absolute values of two opposite quantities will always be the same.

second approach: PLUGGING
just plug in a whole bunch of different sets of x/y/z that satisfy statement (1). i.e., x and y must be the same number, but z can be any number at all (since there are no restrictions on z in the statement).
if you plug in enough sets of numbers, you'll notice the pattern -- the absolute values will always have opposite numbers inside them, and so they will always be the same once the absolute value makes them positive.

[royaamir]

Thank you Very Much!!!!

[jnelson0612]

Thanks Ron!

[rachelhong2012]

rephrase the question:

is X-Z = Z-Y? OR X-Z= Y-Z which can be rephrased as X=Y? (as long as the statement satisfies either condition, it is suff)

1. X=Y suff

2. abs (x) = abs (Y)
could turn out to be:
x=y or x=-y
The first condition satisfies the question, but the second condition doesn't, so it depends on which condition you get. thus it's a maybe to the question, insuff.

[RonPurewal]

rachel, yes.