Express y in terms of x Question:
$$
\text{It is given that } y= \frac{3a+2}{2a-4} \text{and }x= \frac{a+3}{a+8} \\
$$ 
$$
\text{Express } y \text{ in terms of } x.
$$
From using $x$ to solve for $a$, I discovered that 
$$
a = \frac{8x-3}{1-x}
$$
Then I proceeded to substitute $a$ into $y$. I did this twice to ensure no mistakes are made, and my final answer for both was 
$$
\frac{22x-7}{20x-10}
$$
There's a problem, the correct answer is 
$$
\frac{7-22x}{10-20x}
$$
This makes me want to cry, more so because I checked it twice and I was very careful about my working out, here it is:
$$
\frac{2+ 3(\frac{8x-3}{1-x})}{  2(\frac{8x-3}{1-x}) -4  }
$$
$$\rightarrow{}$$
$$
\frac{(\frac{2(1-x) + 3(8x-3)}{1-x})}{(\frac{-4(1-x)+2(8x-3)}{1-x})}
$$
$$\rightarrow{}$$
$$
\frac{2(1-x) + 3(8x-3)}{1-x} * \frac{1-x}{-4(1-x)+2(8x-3)}
$$
$$\rightarrow{}$$
$$
\frac{22x-7}{1-x} * \frac{1-x}{20x-10}
$$
The $(1-x)$'s cancel out
$$\rightarrow{}$$
$$
\frac{22x-7}{20x-10}
$$
Can someone please tell me as to what I did incorrectly in the process? Thank you in advance!

You got the correct answer. Just multiply both numerator and denominator by -1
$$\frac{22x-7}{20x-10} = \frac{-1}{-1} \times \frac{7-22x}{10-20x}$$
