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To solve this expression, we can begin by simplifying it step by step:
First, we distribute the factors outside of the parentheses:
(1/2)(z+4) - 3(1/4z + 1)
Next, we simplify each term:
(1/2)z + (1/2)(4) - (3/4)z - 3
Now, simplify the constant terms:
(1/2)z + 2/2 - (3/4)z - 3
Next, simplify the fractions by finding a common denominator:
(2/4)z + 2/2 - (6/4)z - 3
Combine like terms:
(2/4 - 6/4)z + 2/2 - 3
Simplify further:
(-4/4)z + 2/2 - 3
Simplify the fractions again:
-1z + 1 - 3
Combine the constant terms:
-z - 2
Therefore, the simplified expression is -z - 2.