Subtract 1/2(z + 4) - 3(1/4z + 1). Use fractions in final form.

Answer 1

To subtract 1/2(z + 4) - 3(1/4z + 1), let's simplify each term step by step:

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

3(1/4z + 1) = 3 * 1/4z + 3 * 1 = 3/4z + 3

Now, we can subtract the two simplified terms:

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

To subtract fractions, we need to have a common denominator. In this case, the common denominator is (2 * 4 = 8):

(4/8z + 16/8) - (6/8z + 24/8)

Now, we can combine like terms:

(4z + 16) / 8 - (6z + 24) / 8

= (4z - 6z + 16 - 24) / 8

= (-2z - 8) / 8

= -2z/8 - 8/8

= -z/4 - 1

Therefore, the final simplified form of 1/2(z + 4) - 3(1/4z + 1) is -z/4 - 1.