Let's solve for x in the given equation:

0.5(x+5) = 5/6(11-x)

First, distribute the coefficients:

0.5x + 0.55 = 5/611 - 5/6x

Simplify both sides of the equation:

0.5x + 2.5 = 55/6 - 5/6x

Combine like terms:

0.5x + 5/6x = 55/6 - 2.5

1.000x = 52/6 + 25/6

1.000x = 77/6

Now, multiply both sides by 6 to solve for x:

61.000x = 6(77/6)

6x = 77

x = 77/6

Therefore, x = 12.8333 or approximately 12.83.