To solve this equation, we need to first find a common denominator for all the fractions.

3 1/8 is the same as 25/8.
1 5/6 is the same as 11/6.
17/18 is already in the form of a fraction.
4 7/24 is the same as 103/24.

Now, the equation becomes:

25/8 - 103/24 = 17/18 + 11/6

To add the fractions on the right side, we need to find a common denominator. The common denominator is 24:

25/8 - 103/24 = (17/18 24/24) + (11/6 4/4)
25/8 - 103/24 = 408/432 + 44/24
25/8 - 103/24 = 408/432 + 198/432
25/8 - 103/24 = 606/432

Next, we can add the fractions on the right side of the equation:

25/8 - 103/24 = 606/432
25/8 - 103/24 = 303/216

Now, we have:

303/216 = 25/8 - 103/24

To solve for x, we find a common denominator for 25/8 and 103/24, which is 24:

25/8 = 75/24
103/24 = 103/24

Now, the equation becomes:

75/24 - 103/24 = 303/216

To subtract the fractions on the left side, we get:

-28/24 = 303/216

We can simplify the fraction on the left side:

-28/24 = -7/6

Therefore, the solution to the equation is:

x = -7/6.