<s>[INST] How can I solve: $\frac {3x-2}2 - \frac {4x-5}3=2$? I am a a student and I am having difficulty with answering this question. I keep getting $6$ as my value for x  whereas it is wrong. Please may I have a step by step solution to this question so that I won't have difficulties with answering these type of questions in the future.
Question: Solve $$\frac {3x-2}2 - \frac {4x-5}3=2$$
This is what I did to get the answer:
$$2(3x-2) - 3(4x-5) = 12$$
 $$6x-4 - 12x+15 = 12$$
$$6x - 12x = 12+4-15$$
$$-6x = 1$$
$$x = -6 $$
Kind Regards help would be appreciated
 [/INST] Notice that $$\frac{ 3x-2}{2} - \frac{4x-5}{3} = 2$$ is the same as 
$$\ \frac{3\times( 3x-2)}{3  \times 2} -  \frac{2\times(4x-5)}{2\times3} = 2$$
or equivalently 
$$\ \frac{   9x-6 }{6} -  \frac{ 8x-10 }{6} = 2$$
which is the same as 
 $$  \frac{   (9x-6)-(8x-10) }{6}  = 2$$
so we get
$$(9x-6)-(8x-10) =12 $$
so $$x=8 $$
</s>