ubtract 1/2(z+4)−3(1/4 z+1)

Question

. Use fractions in final form.

Answer 1

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

1. Distribute \( \frac{1}{2} \) and \( -3 \):

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

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

2. Combine the two parts:

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

3. Combine the \( z \) terms and the constant terms:

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

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

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

Thus,

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

5. Combine the constant terms:

\[ 2 - 3 = -1 \]

6. So the final expression is:

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

Thus, the final result is

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