Let's solve the inequality step by step:

Distribute the terms on both sides of the inequality:
4x - 21x + 35 ≥ 4 - 12x + 21

Simplify the equation:
-17x + 35 ≥ 25 - 12x

Add 12x to both sides to isolate the variable on one side:
-5x + 35 ≥ 25

Subtract 35 from both sides to isolate the variable:
-5x ≥ -10

Divide by -5 on both sides to solve for x:
x ≤ 2

Therefore, the solution for the inequality 4x - 7(3x-5) ≥ 4 - 3(4x-7) is x ≤ 2.