To solve this inequality, we can start by rewriting it in a more manageable form:

9^(2x+1) + 13^(2x+1) <= 22*117^x

Since 117 = 9*13, we can rewrite the inequality as:

9^(2x+1) + 13^(2x+1) <= 22(913)^x

Next, let's simplify the right-hand side of the inequality:

22(913)^x = 229^x13^x

Now the inequality becomes:

9^(2x+1) + 13^(2x+1) <= 229^x13^x

Divide both sides by 9^x*13^x to get:

(9^(2x+1))/(9^x) + (13^(2x+1))/(13^x) <= 22

Now simplify the expression inside the parentheses:

9^(2x)9 / 9^x + 13^(2x)13 / 13^x <= 22

9^(x)9 + 13^x13 <= 22

Simplify further:

9^(x+1) + 13^(x+1) <= 22

Therefore, the inequality is:

9^(x+1) + 13^(x+1) <= 22

This is the final form of the inequality.