Final answer:
To simplify 1/2x - 5/3y + 3/2x - 2/3y, we combine the like terms for x and y to get the simplified expression 2x - 7/3y.
Step-by-step explanation:
To simplify the expression 1/2x - 5/3y + 3/2x - 2/3y, we need to combine like terms. The like terms in this expression are those with x and those with y.
We combine the terms containing x as follows:
- (1/2x) + (3/2x) = (1+3)/2x = 4/2x = 2x
We then combine the terms containing y:
- (-5/3y) - (2/3y) = (-5-2)/3y = -7/3y
When we put it all together, our simplified expression becomes 2x - 7/3y.