Hello everyone:

Another good question that a student just sent me (you can tell it's getting close to test day for a few of my students!):

QUESTION:

If xy+z=x(y+z) wich must be true?

1-X=0 and Z=0
2-X=1 OR Y=1
3-Y=1 OR Z=0
4-X=1 OR Y=0
5-X=1 OR Z=0

this should be easy and I got it right, but I cant remember what I did to get it right...






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My response:

Good question – here I think it’s probably best to just use the algebra because you can start to anticipate that a few terms will cancel:

xy + z = xy + xz (distribute the multiplication)
-xy = -xy (eliminate the xy terms on both sides to get:)
z = xz

Now, you can either look at it and make your decision (if x = 1, then you just have z = z; or if z = 0, then you have 0 = 0) or you can finish the algebra:

xz – z = 0
z(x – 1) = 0
either z = 0 or x = 1

So answer choice E is correct – either x = 1 or z = 0.