To solve this equation, we need to first distribute the coefficients:

(4 - 7x) / 15 + (1 - x) = 4 - (2x + 1) / 5

Now, let's simplify each side:

(4 - 7x) / 15 + (1 - x) = 4 - 2x/5 - 1/5
(4 - 7x) / 15 + (1 - x) = 19/5 - 2x/5

Next, let's get rid of the fractions by multiplying everything by 15:

15 [(4 - 7x) / 15 + (1 - x)] = 15 [19/5 - 2x/5]

4 - 7x + 15 - 15x = 57 - 6x

Combine like terms:

19 - 22x = 57 - 6x

Now, isolate the variable:

19 - 22x + 6x = 57
19 - 16x = 57
-16x = 57 - 19
-16x = 38
x = 38 / -16
x = -2.375

Therefore, the solution to the equation is x = -2.375.