1/2 (z + 4) - 3 (1/4 z + 1 ) use fractions in final form

To simplify the expression, we can distribute the coefficients to the terms inside the parentheses:

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

Simplifying further:

1/2z + 2/2 - 3/4z - 3

Next, we can combine like terms:

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

To combine the fractions, we need to find a common denominator for the z terms. The common denominator for 2 and 4 is 4:

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

Now that the denominators are the same, we can combine the z terms:

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

Simplifying the remaining fractions:

-1/4z + 1 - 3

Finally, we can combine the integers:

-1/4z - 2.