The given inequalities are:

1) x - 4 < 8 ÷ (2x + 5)

2) 8 ÷ (2x + 5) < 13 ÷ (3 - x)

3) 13 ÷ (3 - x) > 1

To solve these inequalities, we can simplify each one individually:

1) x - 4 < 8 ÷ (2x + 5)
x - 4 < 4 / (x + 2.5)
(x - 4)(x + 2.5) < 4
x^2 - 1.5x - 10 < 0
(x - 2)(x + 5) < 0
-5 < x < 2

2) 8 ÷ (2x + 5) < 13 ÷ (3 - x)
8 / (2x + 5) < 13 / (3 - x)
8(3 - x) < 13(2x + 5)
24 - 8x < 26x + 65
0 < 34x + 41
-41/34 < x

3) 13 ÷ (3 - x) > 1
13 / (3 - x) > 1
13 > 3 - x
x > -10

Combining the solutions of the three inequalities, we get:

-10 < x < -5

Therefore, the solution set for x is -10 < x < -5.