To solve the equation 8.25 - x = 3 1/6 + (-9/10), we need to simplify both sides of the equation and then solve for x.

First, let's simplify the right side of the equation:
3 1/6 can be converted to an improper fraction:
3 1/6 = 3 + 1/6 = 18/6 + 1/6 = 19/6

Next, let's simplify the left side of the equation:
8.25 - x

To subtract a fraction from a decimal, we need to convert the decimal to a fraction. Since 8.25 is already in decimal form, we can convert it to a fraction by writing it as 8 25/100 and simplifying:
8 25/100 = 8 + 25/100 = 800/100 + 25/100 = 825/100

Now, the equation becomes:
825/100 - x = 19/6 - 9/10

To add or subtract fractions, we need a common denominator. The least common multiple of 100 and 6 is 300, so let's rewrite the equation with a common denominator of 300:
(825/100) * (3/3) - x = (19/6) * (50/50) - (9/10) * (30/30)
(2475/300) - x = (950/300) - (270/300)

Now, we can combine the fractions on the right side of the equation:
(2475/300) - x = (950 - 270)/300
(2475/300) - x = 680/300

To solve for x, we need to isolate it on one side of the equation. Let's subtract (2475/300) from both sides:
(2475/300) - (2475/300) - x = (680/300) - (2475/300)
0 - x = (680 - 2475)/300
-x = -1795/300

To simplify the right side of the equation, we can divide both the numerator and denominator by 5:
-x = -359/60

Finally, let's solve for x by multiplying both sides of the equation by -1:
x = 359/60

Therefore, the solution to the equation 8.25 - x = 3 1/6 + (-9/10) is x = 359/60.