9x^2 - 1 < 2x + 9x^2 - 8
Simplify the inequality:
8x^2 - 9 < 2x
Rearrange the inequality:
8x^2 - 2x - 9 < 0
Factor the quadratic equation:
(4x - 3)(2x + 3) < 0
Now, find the solutions:
4x - 3 = 0 or 2x + 3 = 0
4x = 3 or 2x = -3
x = 3/4 or x = -3/2
Since the inequality is less than 0, we'll find the solution between the two values:
-3/2 < x < 3/4

Therefore, the solution to the inequality (3x-1)(3x+1) <= 2x+9x^2-8 is -3/2 < x < 3/4.