To solve each of these equations for the respective variables, we will isolate them one by one.

1) 3/5 + x = 4/5y - 2/7

First, let's isolate x by subtracting 3/5 from both sides:
x = 4/5y - 2/7 - 3/5
x = 4/5y - 2/7 - 9/35
x = 4/5y - (10/35 + 9/35)
x = 4/5y - 19/35

2) 7/25 - k = 7/25d + 2/9

To isolate k, we will subtract 7/25d and 2/9 from both sides:
-k = 7/25d + 2/9 - 7/25
-k = 7/25d + 2/9 - 7/25
-k = 7/25d + (2/9 - 7/25)
-k = 7/25d + (10/45 - 21/45)
-k = 7/25d - 11/45
k = -7/25d + 11/45

3) 1/9 + 7/9 = 3/5d + 2/9

To isolate d, we will first combine the fractions on the left side:
8/9 = 3/5d + 2/9

Next, subtract 2/9 from both sides to isolate 3/5d:
8/9 - 2/9 = 3/5d
6/9 = 3/5d
2/3 = 3/5d

Now, divide both sides by 3/5 to solve for d:
d = (2/3) / (3/5)
d = (2/3) * (5/3)
d = 10/9

Therefore, the solutions to the equations are:
1) x = 4/5y - 19/35
2) k = -7/25d + 11/45
3) d = 10/9