How to simplify the inequality $5c * 3^{n-2} + 3 \le c3^n$ I'm stuck on trying to simplify the inequality:
$5c * 3^{n-2} + 3 \le c3^n$
I'm looking for an expression such as $c \ge x$ without the n
to show when this inequality holds true
Edit:
This inequality arises in the context of solving a recurrence relation with the substitution method.
I just need to show this inequality holds for $n \ge 2$
Logically I can see that if c = 1, $5*3^{n-2} +3 \le 3^n$ holds for $n \ge 2$ but not sure how to prove it explicitly.

Just note $$5c*3^{n-2}+3\le c3^n$$ $$\iff c(3^{n-1}-5\cdot3^{n-3})\ge 1$$ $$\iff 4\cdot3^{n-3}c\ge 1,$$ $$c\ge\frac{1}{4\cdot3^{n-3}}$$
If we need this inequality holds for all positive integer $n$ then we have $c\ge\frac{9}{4}$.
