equation solving – How to remove constants from Reduced result?

I am trying to Reduce some equations and get the final simplified answer. But there are two issues. I appreciate if someone can help me to learn and fix,
This is just an example to show what my problem is, there are lots of similar samples with same issue for me

Reduce(((x >= xP && Mod(x, Abs(1)) == Mod(xP, Abs(1)) && x >= xP && 
     t == tP && z + 2*x*t == zP + 2*xP*tP)) && Not((xP != 10)), {t, 
  xP, zP})

and this the (copy/pasted) output:

C(1) (Element) Integers && C(1) >= 10 && x == C(1) && t == tP && 
 xP == 10 && zP == -20 tP + 2 t x + z

1- how to get rid of these constants? c1 is integer, c>=10 and x==c1 so I expect to just see x>=10; I think there must some other functions to give us a nicer output
2- why doesn’t it replace t and tP? I don’t want to see t==tP, we expect only replacement.