Question

1/2(z + 4 ) - 3 ( 1/4z + 1 ) Use fractions in final from

Answer 1

Let's simplify the expression step by step:

Given expression:

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

First, distribute \(\frac{1}{2}\) in the first term:

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

Now distribute \(-3\) in the second term:

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

Now combine these results:

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

Next, combine like terms. Combine the \( z \) terms first:

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

To combine these, convert \(\frac{1}{2}z\) to a fraction with a denominator of 4:

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

Now we can combine:

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

Now combine the constant terms:

\[
2 - 3 = -1
\]

Putting it all together, the simplified expression is:

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

Thus, the final result is:

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