To solve this inequality, we need to first rewrite it in exponential form:

0.5^(2x+1) >= 0.5^(3x-4)

Now we can drop the base and set the exponents equal to each other:

2x + 1 >= 3x - 4

Now we can solve for x:

2x + 1 >= 3x - 4
2x - 3x >= -4 - 1
-x >= -5
x <= 5

Therefore, the solution to the inequality is x <= 5.