To solve the equation -7/8 - (x + 1/2) = 4/5, we can start by simplifying the equation:

-7/8 - (x + 1/2) = 4/5

To simplify the expression within the parentheses, we can distribute the negative sign:

-7/8 - x - 1/2 = 4/5

Now, let's combine like terms:

-7/8 - 1/2 - x = 4/5

To add the fractions, we need to find a common denominator. The common denominator for 8 and 2 is 8, so we can rewrite the equation as:

-7/8 - 4/8 - x = 4/5

Now, let's combine the fractions:

-11/8 - x = 4/5

To get rid of the fraction, we can multiply both sides of the equation by 40 (the least common multiple of 8 and 5):

40 * (-11/8 - x) = 40 * (4/5)

Simplifying both sides:

-55 - 40x = 32

Now, let's isolate the variable x by moving the constant term to the other side:

-40x = 32 + 55

-40x = 87

Finally, divide both sides by -40 to solve for x:

x = 87 / -40

Simplifying the fraction:

x = -87/40

Therefore, the solution to the equation -7/8 - (x + 1/2) = 4/5 is x = -87/40.