Given AB<CD

Prove that 2AB<2CD

I know that we need to use Archimedes' axiom to prove this but I'm not exactly sure how to do that. The axiom states:

If CD is any segment, A any point, and r any ray with verte A, then for every point B unequal to A on r starting at A, a point E is reached such that n times CD is congruent to AE and either B=E or B is between A and E