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

Answer 1

To subtract the expressions \( \frac{1}{2}(z+4)-3(\frac{1}{4}z+1) \), we'll distribute the coefficients to the terms inside the parentheses first:

\[
\frac{1}{2}(z) + \frac{1}{2}(4) - 3(\frac{1}{4}z) - 3(1)
\]

Simplify each part:

\[
\frac{1}{2}z + 2 - \frac{3}{4}z - 3
\]

Now we need to combine like terms. To do this with the \(z\) terms, which have different coefficients, we need to find a common denominator. The LCD for 2 and 4 is 4, so we convert the first term \(\frac{1}{2}z\) to a fraction with 4 as the denominator:

\[
\frac{1}{2}z = \frac{2}{4}z
\]

Substitute this back into the expression:

\[
\frac{2}{4}z + 2 - \frac{3}{4}z - 3
\]

Now subtract the \(z\) terms:

\[
(\frac{2}{4}z - \frac{3}{4}z) + 2 - 3
\]
\[
= \frac{-1}{4}z + 2 - 3
\]

Finally, subtract the constants:

\[
\frac{-1}{4}z + (2 - 3)
\]
\[
\frac{-1}{4}z - 1
\]

In final fractional form:

\[
-\frac{1}{4}z - \frac{1}{1}
\]

This is the simplified form of the original expression with the subtraction applied and the terms combined.