Final answer:
The expression 3x-1/2y+2 2/3 y-5/6x can be simplified to (13/6)x + (11/6)y.
Step-by-step explanation:
The expression 3x-1/2y+2 2/3 y-5/6x can be simplified by combining like terms and performing the necessary operations. To do this, we first need to find a common denominator for the fractions. The common denominator for 1/2 and 2/3 is 6, so we rewrite the equation as:
3x - (1/2)y + (2 2/3)y - (5/6)x
Now, we combine the x and y terms:
3x - (5/6)x - (1/2)y + (2 2/3)y
Next, we simplify the mixed number:
3x - (5/6)x - (1/2)y + (8/3)y
Finally, combining like terms:
(3 - 5/6)x + (8/3 - 1/2)y
This gives us the simplified expression of (13/6)x + (11/6)y.