I'm having trouble understanding how to prove this problem. I need some help.

Let x Real number and Let S be a non empty subset of real numbers that is bounded above. We define a new set x + S, by x+S={x+s: s S}

a) Prove that x +S is bounded above

b) Prove that x + sup(S) is an upper bound of x + S. Conclude that the sup(x+ S) ≤ x + sup(S)

C) Prove that x + sup(S) = sup(S) = sup(x+S)

Thanks for any help provided.