To solve the equation 1 1/2 - (5/6)x + 1/3 = 8/9, we first need to convert the mixed number 1 1/2 to an improper fraction:
1 1/2 = 3/2 + 1/2 = 4/2 = 2
Now we can substitute all the values into the equation:
2 - (5/6)x + 1/3 = 8/9
We can simplify the equation by multiplying everything by the least common multiple of the denominators of the fractions, which is 18:
36 - 15x + 6 = 16
Subtracting 6 from both sides gives:
30 - 15x = 16
Subtracting 30 from both sides gives:
-15x = -14
Dividing both sides by -15 gives:
x = 14/15
Therefore, the solution to the equation is x = 14/15.