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

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

Simplify the equation by converting the bases to the same value:

(0.5^3)(0.5^(-2x)) > 4

0.5^3 = 0.125
4 = 2^2

0.125(0.5^(-2x)) > 2^2

0.125 * (1 / (0.5^2x)) > 4

0.125 / 0.25^x > 4

0.5^x > 32

Now we can rewrite the inequality in terms of logs:

x > log0.5 32

x > log 32 / log 0.5

x > 5

Therefore, the solution to the inequality is x > 5.