4,5(x-2)-(x-4)=15-3(x+1)

Expanding the left side:

4,5x - 9 - x + 4 = 15 - 3x - 3

Combining like terms:

3,5x - 5 = 12 - 3x

Adding 3x to both sides:

6,5x - 5 = 12

Adding 5 to both sides:

6,5x = 17

Dividing by 6.5 to solve for x:

x = 17/6.5 = 2.6154

Therefore, the solution to the equation is x = 2.6154.