To solve each equation, we need to isolate the variable inside the absolute value and then solve for x.

1) |2 + 7x| = 0
The absolute value of any number is always non-negative, so the absolute value of any number cannot be equal to 0 unless the number inside the absolute value is 0.
Therefore, we have 2 + 7x = 0
Solving for x:
7x = -2
x = -2/7

2) |8x - 5| = 0
Similarly, the absolute value of any number cannot be equal to 0 unless the number inside the absolute value is 0.
Therefore, we have 8x - 5 = 0
Solving for x:
8x = 5
x = 5/8

3) |9 - 10x| = 0
Using the same principle, we have 9 - 10x = 0
Solving for x:
10x = 9
x = 9/10

Therefore, the solutions to the given equations are:
1) x = -2/7
2) x = 5/8
3) x = 9/10