8) Write prove for below;

a. For all of real numbers a, b, and c, there is a real number x so that x+ a = 5x + b + c.

b. For every real number x, if x^3 is irrational then x is irrational (use contradiction)

Definitions:

Real number x is rational if there are integers p and q such that x = p / q

Real number x is irrational if x is not rational