First, let's simplify the left side of the inequality:

0.2x(x-1) - x(0.2x + 0.5)
= 0.2x^2 - 0.2x - 0.2x^2 - 0.5x
= -0.7x

Now, let's simplify the right side of the inequality:

0.6 - 4
= -3.4

So the inequality becomes:

-0.7x < -3.4

To solve for x, divide both sides of the inequality by -0.7 (and remember to reverse the inequality sign when dividing by a negative number):

x > 4.857

Therefore, the solution to the inequality is x > 4.857.