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

Answer 1

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

1. Distribute \(-\frac{1}{2}\) for the first term:

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

2. Distribute \(-3\) for the second term:

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

3. Now combine these results:

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

4. Combine the \(z\) terms and the constant terms separately:

The \(z\) terms: \[ -\frac{1}{2}z - \frac{3}{4}z \]

To combine these, first convert \(-\frac{1}{2}z\) to have a denominator of 4: \[ -\frac{1}{2}z = -\frac{2}{4}z \]

Now we can add: \[ -\frac{2}{4}z - \frac{3}{4}z = -\frac{2 + 3}{4}z = -\frac{5}{4}z \]

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

5. Therefore, the final expression is:

\[ -\frac{5}{4}z - 5 \]

So, the final simplified expression in fraction form is:

\[ -\frac{5}{4}z - 5 \]