Discrete Math - Strong Induction Question

[Rosebud]

Homework Statement

Prove by Strong Mathematical Induction[/B]

Homework Equations

N/A

The Attempt at a Solution

The steps to solving this problem are shown below. I understand all steps of the problem until the part where it says 44/49 becomes 49/49 since 44 < 49. Can someone please explain the logic behind that step? Thank you.

 

[FactChecker]

If a>0 then a*(44/49) < a*(49/49).
Sort of like saying that f(x) = ax is strictly increasing.