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
 A: 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 $$x=8 $$
A: The mistake you made is that you didn't cross multiply. Instead of doing:
\begin{align}
\frac{\color{#f00}3}{\color{#f00}3} \cdot \frac {(3x-2)}{\color{#0000ff}2} - \frac{\color{#0000ff}2}{\color{#0000ff}2} \cdot \frac {(4x-5)}{\color{#f00}3}=2
\end{align}
You did
\begin{align}
\frac {2(3x-2)}{2} - \frac {3(4x-5)}{3} &= 2 \\
\frac {2(3x-2)}{6} - \frac {3(4x-5)}{6} &= 2 \\
{2(3x-2)} - {3(4x-5)}&=12 \\
...
\end{align}
So you noticed that we need to combine the fractions but you didn't combine them properly. If you want to get the same denominator then you need to find a common multiple of the denominators of your fractions. The easiest way to do that is to cross multiply. 
Can you solve it from here?
\begin{align}
\frac {3(3x-2) - 2(4x-5)}{6} =2
\end{align}
Let me know if you have any further questions!
A: Step 1: Get the same denominator, 6, for both terms.
$\frac33*\frac{3x-2}2 - \frac22 * \frac{4x-5}3 = \frac{9x-6}6 - \frac{8x-10}6 = 2$
Step 2: Combine terms
$\frac{9x-8x-6+10}6 = \frac{x+4}6 = 2$
Step 3: Solve for x
$x+4 = 12$
$x=8$
A: There are different ways you could solve for $x;$ here is one way:
$\frac{3x-2}{2} - \frac{4x-5}{3} = 2 \rightarrow$
$\frac{3}{2}x - 1 - (\frac{4}{3}x - \frac{5}{3}) = 2 \rightarrow$
$\frac{1}{6}x + \frac{2}{3} = 2 \rightarrow$
$\frac{1}{6}x = \frac{4}{3} \rightarrow$
$x = 8$
