How would I work this problem out if I did not want to cross multiply?
$\displaystyle \frac{18-5x}{3x+2}=\frac{7}{3}$
I would think we should start with the LCD 3(3x+2) no?
Is this what your trying to do with the LCD?
$\displaystyle \frac{18-5x}{3x+2}=\frac{7}{3}$
$\displaystyle \frac{18-5x}{3x+2}-\frac{7}{3}=0$
$\displaystyle
\frac{3(18-5x)-7(3x+2)}{3(3x+2)}=0
$
Because this still gives you
$\displaystyle 3(18-5x)-7(3x+2)=0$
Which is the same as cross multiplying and dividing which gives
$\displaystyle
3(18-5x)=7(3x+2)
$
So you could do it that way, but it's much more work.