How do you prove this implication using its contrapositive?

Question

$∀x∈R,|2x-1|≤5$ and $|2x-1|>3⇒(x^4+7≤7x^2 )$ or $(2x^3≥8x+5)$

This is what I got for the contrapositive:

$∀x∈R,(x^4+7>7x^2 )$ and $(2x^3<8x+5)⇒|2x-1|>5$ or $|2x-1|≤3$

Where would I go from here? How would I combine the 'and' logical connective?