Algebra Question

[Spartacus2000]

If xy + z = x(y+z), which of the following must be true?

a. x = 0 and z = 0
b. x = 1 and y = 1
c. y = 1 and z = 0
d. x = 1 or y = 0
e. x = 1 or z = 0

The correct answer given is (e).

Do the values of x and z have to be tested seperately?

[SoCan]

xy+z=x(y+z)
xy+z=xy+xz
z=xz

This holds when x=1 or z=0.

[cans]

xy+z = x(y+z)
xy+z = xy+xz
xz-z=0 => z(x-1)=0
Thus either z=0 or x=1.

[MBA.Aspirant]

xy + z = x(y+z)

xy+z = xy + xz

z = xz

Z = 0 or x = 1