prove the equivalence of the following statements: 2x-1 is irrational; x/3 is irrational

Question

I am stumped. I really have no idea how to solve this problem. Can someone please help me through this? THE TWO EQUATIONS ARE SEPERATE

Answer 1

Updated to match corrected problem.

HINT: If $\frac{x}3$ were rational, $3\cdot\frac{x}3$ would be rational as well. (Why?) Extend this idea to show that $2x-1$ would be rational. This shows that if $2x-1$ is irrational, so is $\frac{x}3$. Then reverse the procedure to get the opposite implication.

Answer 2

Hint: Let $y=2x-1$ and $z=x/3$. Then $2x=y+1=6z$. Based on that last equality, what does the rationality of $y$ imply about that of $z$ (and vice versa)?