Question

how do I solve using the multiplacation method

-2x>1/9

Answer 1

I guess that means that you multiply both sides by the reciprocal of the coefficient thusly:

-2x * 1/-2 < 1/9 * 1/-2

x < -1/18

Have you wondered why multiplying by a negative flips the direction of the inequality? It's just a shorthand way of moving items to the other side.

-2x < 4

Now suppose you want +2x: Just add 2x to each side

-2x + 2x < 4 + 2x
0 < 4 + 2x
Now subtract 4 from both sides:
-4 < 2x

But that's the same as

2x > -4

which is what you get by multiplying by -1 and swapping direction.