To solve the equation 2/5m + 3/5m - 2/15 = 1/6, we first combine like terms:

(2/5 + 3/5)m - 2/15 = 1/6
(5/5)m - 2/15 = 1/6
m - 2/15 = 1/6

Next, we add 2/15 to both sides:

m - 2/15 + 2/15 = 1/6 + 2/15
m = 5/30 + 4/30
m = 9/30
m = 3/10

Therefore, the solution to the equation is m = 3/10.

Next, to solve the equation z - 8/15z = 1/3, we combine like terms:

z - 8/15z = 1/3
(1 - 8/15)z = 1/3
(15/15 - 8/15)z = 5/15
(7/15)z = 5/15

Now, we divide both sides by 7/15:

z = (5/15) / (7/15)
z = 5/15 15/7
z = 1/3 15/7
z = 5/7

Therefore, the solution to the equation is z = 5/7.

Finally, for the equation 5/9x = 1, we solve for x by multiplying both sides by the reciprocal of 5/9 (which is 9/5):

(9/5) (5/9)x = 1 (9/5)
x = 9/5

Therefore, the solution to the equation is x = 9/5 or 1 4/5.