Gauss's Law with a sphere on and charge on z-axis

[ScandelousWenc]

I have a question for E&M and I feel like I am over complicating it. As the title says, the is a positive charge on the x-axis and I must prove that flux = q/εo.

Since the charge is on the z-axis, could I just add in a term (z-z') to account for the charge not being at the origin into calculating ∫E dA?

 

[Simon Bridge]

Welcome to PF;
If you already know an equation is f(x,y,z), then shifting the source a distance z' in the +z direction turns that into f(x,y,z-z') yes.