Question

Math Proof: Prove that for all real numbers x and y there is a real number z such that x+z=y-z

Answer 1

well the difference of real numbers is a real number
also \[z=\frac{y-x}{2}\]

Answer 2

Shouldn't I be finding what x and y equal to prove the equation?

Answer 3

x and y are all real numbers

Answer 4

it says that in the question

Answer 5

Ah so i have to find Z.

Answer 6

Then would I have to plug z back into the equation to prove it?

Answer 7

well you have to prove that z is real

Answer 8

Hrmm... How would I do that?

Answer 9

well the difference of real numbers is a real number
and a real number divided by 2 is a real number

Answer 10

and z must be half the difference between y and x from the equations

Answer 11

I understand that, but now how would I prove that x+z = y-z?

Answer 12

substitute for z