First, let's simplify the equation by combining like terms:

0.5x - 1/6x = 2 1/2

To combine the terms, we need to find a common denominator for the fractions. The common denominator for 6 and 2 is 6.

0.5x - (1/6)x = 5/2

Now we can combine the terms by multiplying the fractions by 6 to get rid of the denominators:

3x/6 - 1x/6 = 5/2

Now we can simplify the equation:

(3x - 1x)/6 = 5/2

2x/6 = 5/2

Now, multiply both sides by 6 to get rid of the fraction:

2x = 15

Finally, divide by 2 to solve for x:

x = 15/2

Therefore, the solution to the equation is x = 7.5.