To solve this equation, we first need to combine the constants on the left side of the equation:

x - 3 5/6 + 17/18 = 7 13/24

To combine the constants, we first convert 3 5/6 to an improper fraction:

3 5/6 = 3 + 5/6 = 18/6 + 5/6 = 23/6

Now, we combine the constants:

x - 23/6 + 17/18 = 7 13/24

Next, we need to get a common denominator for the fractions on the left side. The common denominator between 6 and 18 is 18, so we rewrite 23/6 as 23/6 * 3/3 = 69/18:

x - 69/18 + 17/18 = 7 13/24

Now, we add the constants:

x - 52/18 = 7 13/24

To simplify the mixed number on the right side, we convert 7 to a fraction with a denominator of 24:

7 = 7/1

Now, convert the mixed number to a fraction:

7 13/24 = 7 + 13/24 = 168/24 + 13/24 = 181/24

Now, the equation is:

x - 52/18 = 181/24

To isolate x, we add 52/18 to both sides:

x = 181/24 + 52/18
x = (1813 + 524) / (24*3)
x = (543 + 208) / 72
x = 751 / 72

Therefore, the solution to the equation is x = 751/72.