Question

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 will first distribute the coefficients in front of the parentheses.

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

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

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

Next, combine the like terms:
1. For the \( z \) terms:
\[
-\frac{1}{2}z - \frac{3}{4}z
\]
To combine these, we need a common denominator, which is 4. Rewrite \( -\frac{1}{2}z \) as \( -\frac{2}{4}z \):
\[
-\frac{2}{4}z - \frac{3}{4}z = -\frac{5}{4}z
\]

2. For the constant terms:
\[
-2 - 3 = -5
\]

Putting it all together, we have:
\[
-\frac{5}{4}z - 5
\]

Thus, the final simplified form of the expression is:
\[
-\frac{5}{4}z - 5
\]