To solve this equation, we can combine the terms on the left side of the equation by adding the exponents of the common base (0.5).

0.5^(x+7) 0.5^(1-2x) = 0.5^(x+7+1-2x)
0.5^(x+7) 0.5^(1-2x) = 0.5^(8-x)

Now, the equation becomes:

0.5^(8-x) = 2

To solve for x, we can rewrite 2 as a power of 0.5:

0.5^(8-x) = 0.5^-1

Now we can set the exponents equal to each other:

8-x = -1

Solving for x:

8 + 1 = x
9 = x

Therefore, the solution to the equation is x = 9.