1/2(z+5)-3(1/4z+1)

To simplify the expression 1/2(z+5) - 3(1/4z+1), we can distribute the -3 to terms inside the parenthesis:

1/2(z+5) - 3(1/4z+1) = 1/2z + 5/2 - (3/4z + 3)

Next, let's simplify each term separately.

1/2z + 5/2 - (3/4z + 3) = (1/2z - 3/4z) + (5/2 - 3)

Next, let's find a common denominator for the fractions:

(1/2z - 3/4z) + (5/2 - 3) = (2/4z - 3/4z) + (10/4 - 12/4)

Now, let's combine like terms:

(2/4z - 3/4z) + (10/4 - 12/4) = (-1/4z) + (-2/4)

Simplifying further:

(-1/4z) + (-2/4) = -1/4z - 2/4

Since -2/4 can be simplified by dividing both the numerator and denominator by 2, this expression can be simplified to:

-1/4z - 1/2