First, let's solve the equation -2(5-x)=1:

-2(5-x) = 1
-10 + 2x = 1
2x = 11
x = 11/2
x = 5.5

Next, let's solve the equation 5x+0.5(x+4):

5x + 0.5(x+4) = 5x + 0.5x + 2
= 5.5(5) + 0.5(5+4)
= 27.5 + 2.5
= 30

Therefore, x = 5.5 satisfies both equations.