To solve for x, we need to first convert the mixed numbers into improper fractions:

8 7/18 = (18 8 + 7)/18 = 143/18
1 5/8 = (8 1 + 5)/8 = 13/8
2 17/18 = (18 * 2 + 17)/18 = 53/18

Now we can rewrite the equation:

143/18 - x = 13/8 + 53/18

Now, find a common denominator for the fractions on the right side of the equation which is 72:

143/18 - x = (13/8 9/9) + (53/18 4/4)
143/18 - x = 117/72 + 212/72
143/18 - x = 329/72

Now, multiply each fraction by 4 to clear the denominators:

(143/18) 4 - x = (329/72) 4
572/18 - x = 1316/72
31.7778 - x = 18.2778

Now, solve for x:

-x = 18.2778 - 31.7778
-x = -13.5
x = 13.5

Therefore, the value of x is 13.5.