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.