To solve this equation, we need to find a common denominator and combine the fractions on both sides.

The common denominator for 6 and 9 is 18.

So, we rewrite the equation with a common denominator of 18:

((3(2x-3))/18) - ((2(5x-4))/18) = 1
(6x - 9)/18 - (10x - 8)/18 = 1

Now, we combine the fractions:

(6x - 9 - 10x + 8)/18 = 1
(-4x - 1)/18 = 1

Now, isolate x by multiplying both sides by 18:

-4x - 1 = 18
-4x = 19
x = -19/4

So, the solution to the equation is x = -19/4 or -4.75.