Solve for x the inequality: 81^(x-1) - 9^(x+1) > 0

We'll the base of the 1st term as power of
9:

9^2*(x-1) - 9^(x+1) >
0

We'll shift to the left, the 2nd
term:

9^2*(x-1) >
9^(x+1)

Since the bases are bigger than unit value, the
function is increasing and we'll get:

2*(x-1)>
(x+1)

We'll remove the
brackets:

2x - 2 > x +
1

We'll subtract x both
sides:

2x - x - 2 > 1

x
- 2 > 1

We'll add 2 both
sides:

x > 2 + 1

x
> 3

The range of values of x, for the
inequality to hold, is (3 , +infinite).