Let's solve the equation step by step:

5(0.1x - 0.5) + 1.6 = 0.4(x - 3)

First, distribute the 5 on the left side:
0.5x - 2.5 + 1.6 = 0.4x - 1.2

Combine like terms:
0.5x - 0.9 = 0.4x - 1.2

Subtract 0.4x from both sides:
0.1x - 0.9 = -1.2

Add 0.9 to both sides:
0.1x = -1.2 + 0.9
0.1x = -0.3

Divide by 0.1 to solve for x:
x = -0.3 / 0.1
x = -3

Therefore, the solution to the equation is x = -3.