<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] There are different ways you could solve for $x;$ here is one way:
$\frac{3x-2}{2} - \frac{4x-5}{3} = 2 \rightarrow$
$\frac{3}{2}x - 1 - (\frac{4}{3}x - \frac{5}{3}) = 2 \rightarrow$
$\frac{1}{6}x + \frac{2}{3} = 2 \rightarrow$
$\frac{1}{6}x = \frac{4}{3} \rightarrow$
$x = 8$
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