Let's solve this equation step by step:

0.5*(8x + 1) = 1.5 - (9 - 4x)

First, distribute the 0.5 on the left side:

4x + 0.5 = 1.5 - (9 - 4x)

Next, simplify the expression inside the parentheses on the right side:

4x + 0.5 = 1.5 - 9 + 4x

Combine the constants on the right side:

4x + 0.5 = -7.5 + 4x

Subtract 4x from both sides:

0.5 = -7.5

This equation is not possible, so there is no solution.