Subtract 1/2(z+4)−3(1/4z+1). 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 will first distribute the terms inside the parentheses.

1. Distribute \( \frac{1}{2} \) across \( (z + 4) \):

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

2. Distribute \( -3 \) across \( \left(\frac{1}{4}z + 1\right) \):

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

3. Combine both results:

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

4. Combine like terms. First, let's convert \( \frac{1}{2}z \) to a fraction with a denominator of 4:

\[ \frac{1}{2} = \frac{2}{4} \quad \text{so} \quad \frac{1}{2}z = \frac{2}{4}z \]

5. Now we have:

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

6. Combine the \( z \) terms:

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

7. Combine the constant terms:

\[ 2 - 3 = -1 \]

8. Putting it all together, we have:

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

So, the final result is:

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