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

Answer 1

Let's solve the problem step by step:

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

First, distribute the 1/2 and -3:
1/2 * z + 1/2 * 4 - 3 * 1/4 * z - 3 * 1

Simplify each term:

1/2 * z = z/2

1/2 * 4 = 4/2 = 2

3 * 1/4 * z = 3/4 * z

3 * 1 = 3

Now substitute the simplified terms back into the original equation:

z/2 + 2 - 3/4 * z - 3

Now, combine like terms:

z/2 - 3/4 * z + 2 - 3

To combine the fractions, we need to find a common denominator. The least common multiple of 2 and 4 is 4. So, let's rewrite the equation with a common denominator:

(z * 2/2) - (3/4 * z) + 8/4 - 12/4

Simplify the fractions:

2z/2 - 3z/4 + 8/4 - 12/4

Combine the numerators:

(2z - 3z)/4 + (8 - 12)/4

Simplify further:

-z/4 - 4/4

Combine like terms:

(-z - 4)/4

So, the final answer in fraction form is (-z - 4)/4.