x-7/9x=5/12

$${\frac{\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{7}}\right)}{\left({\mathtt{9}}{\mathtt{\,\times\,}}{\mathtt{x}}\right)}} = {\frac{{\mathtt{5}}}{{\mathtt{12}}}}$$

Cross multiply and you will get:

$$12x-84=45x$$

After you get the above just solve for x:

$$-84=33x$$

$$x=-2.5454545454545455$$

So your answer is x=-2.5454545454545455. You can simply that down further to a number like -2.55. 

Excellent answer, chilledz3non......"thumbs-up" from me...

Note something.....x = -84/33 = -28/11.......we could also leave the answer in this form....some people like the "exact" answer, rather than a repeating decimal....I'm actually indifferent, but I might be in the minority......

I definitely prefer exact answers 

But I don't like improper fractions much.  I think that they should be presented as mixed numberals.

If you were able to use the repeating dot notation for a decimal that would also be fine to because that is exact.

A note to anon.

Chris has probably answered the question that you intended to ask BUT

this is the question that you did ask.

x-7/9x=5/12

$$\begin{array}{rll} x-\frac{7}{9}x&=&\frac{5}{12}\\\\ \frac{2x}{9}&=&\frac{5}{12}\\\\ 36\times \frac{2x}{9}&=&36\times \frac{5}{12}\\\\ 8x&=&15\\\\ x&=&\frac{15}{8}\\\\ x&=&1\frac{7}{8}\\\\ \end{array}$$

The motto of this story is USE BRACKETS