Subtract 1/2 [z +4] -3 [1/4 z + 1]. Use fractions in final form.
To subtract fractions, we need a common denominator. In this case, our common denominator will be 4.
First, let's simplify the first term: 1/2 [z + 4]. Distributing the 1/2, we have: (1/2)z + (1/2)(4) = 1/2z + 2.
For the second term: 3 [1/4z + 1]. Distributing the 3, we have: 3(1/4z) + 3(1) = 3/4z + 3.
Now let's subtract the simplified terms: (1/2z + 2) - (3/4z + 3).
To subtract fractions, we need to have the same denominator. In this case, our common denominator is 2*4 = 8.
Multiplying the first term by 4/4 and the second term by 2/2, we have: ((1/2z)*(4/4)+(2)*(4/4)) - ((3/4z)*(2/2)+(3)*(2/2)).
This simplifies to: (4/8z + 8/4) - (6/8z + 6/2).
Now, combining like terms, we have: (4/8z - 6/8z) + (8/4 - 6/2).
Simplifying further, we have: (-2/8z) + (8/4 - 12/4).
This becomes: -2/8z + (-4/4).
Simplifying the second term, we have: -2/8z - 1.
Finally, we can simplify the equation: -2/8z - 1.
So the final answer is -2/8z - 1.