To solve for x, we first want to get rid of the fraction on the right side of the equation. Let's convert 7 1/8 to an improper fraction:

7 1/8 = 8(7) + 1 / 8 = 57/8

So, the equation becomes:

9.625 - 15/(x + 4) = 57/8

Next, let's get rid of the decimal by multiplying everything by 8 to clear the fraction:

8(9.625) - 8(15/(x+4)) = 8(57/8)

76 - 120/(x + 4) = 57

Now, let's isolate the term with the fraction:

-120/(x + 4) = 57 - 76
-120/(x + 4) = -19

To solve for x, multiply both sides by (x + 4):

-120 = -19(x + 4)
-120 = -19x - 76
-44 = -19x
x = 44/19

Therefore, x = 44/19.