I am having difficult time with a contradiction. Here is the simple math problem that I cannot understand why exactly the same technique gives two different (and contradictory) results:

The question is what is the smallest ***x*** value that satisfies the below inequality:

$$(\frac{2}{3})^{2x-1}< (\frac{27}{8})^{x-2}$$

if you rearrange the left item and solve the problem as:

$$(\frac{3}{2})^{-2x+1}<(\frac{3}{2})^{3x-6}$$
$$-2x+1<3x-6$$
$$7<5x$$
$$\frac{7}{5} < x$$ which yields **2** as the answer. However, if you rearrange the right item of the inequality the steps are:

$$(\frac{2}{3})^{2x-1}<(\frac{2}{3})^{6-3x}$$
$$2x-1<6-3x$$
$$5x<7$$
$$\frac{7}{5} > x$$
which yields **1** as the answer. where is the problem? What is the cause of this contradiction?
Thank you.