1/2 (8y- 10z)- (3y+z)

1/2 (8y- 10z)- (3y+z)

4y - 5z - 3y - z

y - 6z

To simplify the expression 1/2 (8y- 10z)- (3y+z), we can follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division [from left to right], Addition and Subtraction [from left to right]).

First, let's distribute the 1/2 to each term inside the parentheses:
1/2 * 8y = 4y
1/2 * (-10z) = -5z

Now the expression becomes:
4y - 5z - (3y+z)

Next, let's simplify the expression inside the parentheses:
4y - 5z - 3y - z

Now we can combine the like terms:
(4y - 3y) + (-5z - z)
y - 6z

So, the simplified expression is y - 6z.