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

Answer 1

To subtract 1/2(z+4) - 3(1/4z+1), we first need to distribute the negative sign in front of the 3 to both terms within the parentheses:

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

This becomes:

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

Now, let's simplify further:

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

To combine like terms, we need to have a common denominator. In this case, the least common denominator is 4:

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

Simplifying:

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

Now, combine the like terms:

(-8z - 4)/4

Finally, simplifying and rewriting in fraction form:

-2z - 1