Question

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

Answer 1

To simplify the expression \( \frac{1}{2}(z + 4) - 3\left(\frac{1}{4}z + 1\right) \), we can follow these steps:

1. Distribute \( \frac{1}{2} \) and \( -3 \) through the respective expressions.
2. Combine like terms.

Let's do it step by step.

1. Distributing \( \frac{1}{2} \) to \( (z + 4) \):
\[
\frac{1}{2}(z + 4) = \frac{1}{2}z + \frac{1}{2} \cdot 4 = \frac{1}{2}z + 2
\]

2. Distributing \( -3 \) to \( \left(\frac{1}{4}z + 1\right) \):
\[
-3\left(\frac{1}{4}z + 1\right) = -3 \cdot \frac{1}{4}z - 3 \cdot 1 = -\frac{3}{4}z - 3
\]

3. Now combine the two results:
\[
\frac{1}{2}z + 2 - \frac{3}{4}z - 3
\]

4. Combine the \( z \) terms:
\[
\frac{1}{2}z - \frac{3}{4}z
\]
To combine these, we can convert \( \frac{1}{2}z \) to a fraction with a denominator of 4:
\[
\frac{1}{2}z = \frac{2}{4}z
\]
Now we can subtract:
\[
\frac{2}{4}z - \frac{3}{4}z = -\frac{1}{4}z
\]

5. Now combine the constant terms:
\[
2 - 3 = -1
\]

Putting it all together, we have:
\[
-\frac{1}{4}z - 1
\]

So, the final answer is:
\[
-\frac{1}{4}z - 1
\]