Proof by working backwards(1)

Write clear and complete proofs by working backwards for the following mathematical statement.
(1) The expression x + 9/x >= for all real numbers x > 0.
(Scratch work)

x + 9/x >= 6

x^2 + 9 >= 6x

x^2 - 6x + 9 >= 0

(x - 3)^2 >= 0

Proof. Assume that x is a real number with x > 0. Then notice that

(x -3)^2 >= 0

x^2 - 6x +9 >= 0

x^2 + 9 >= 6x

x + 9/x >= 6x.

QED