Alex, this is the solution to the problem:
As you can read in the hint given, angles L and M are supplementary. That means that their sum add up to 180 degrees.
Upon saying that, we have:
7x - 9 + 9x - 3 = 180
16x - 12 = 180
Adding 12 at both sides:
16x - 12 + 12 = 180 + 12
16x = 192
Dividing by 16 at both sides:
16x/16 = 192/16
x = 12
Now, we can find the measure of the angles, as follows:
L = 7x - 9
L = 7 * 12 - 9
L = 84 - 9
L = 75
M = 9x - 3
M = 9 * 12 - 3
M = 108 - 3
M = 105