Question

Subtract \(\frac{1}{2}\left(z+4\right)-3\left(\frac{1}{4}z+1\right)\). Use fractions in final form.
(1 point)

Answer 1

To subtract the expression \(\frac{1}{2}(z+4)-3\left(\frac{1}{4}z+1\right)\), we first distribute the terms inside the parentheses.

1. Distribute \(\frac{1}{2}\) in the first part:

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

2. Distribute \(-3\) in the second part:

\[
-3\left(\frac{1}{4}z+1\right) = -3 \cdot \frac{1}{4}z - 3 \cdot 1 = -\frac{3}{4}z - 3
\]

3. Now we can combine both distributed results:

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

4. Combine like terms, starting with the \(z\) terms:

To combine \(\frac{1}{2}z - \frac{3}{4}z\), we need a common denominator. The common denominator of 2 and 4 is 4.

Convert \(\frac{1}{2}z\) to a fraction with a denominator of 4:

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

Now we subtract:

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

5. Now combine the constant terms \(2 - 3\):

\[
2 - 3 = -1
\]

6. Putting it all together:

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

Thus, the final result of the expression is:

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