Question

Subtract 12(z+4)−3(14z+1)
1
2
(
𝑧
+
4
)
−
3
(
1
4
𝑧
+
1
)
. Use fractions in final form.(1 point)....................

Answer 1

Let's simplify the expression step by step:

Given:

\[
12(z + 4) - 3(14z + 1)
\]

1. Distribute the 12 and -3:

\[
12(z) + 12(4) - 3(14z) - 3(1)
\]

This simplifies to:

\[
12z + 48 - 42z - 3
\]

2. Combine like terms:

Combine \(12z\) and \(-42z\):

\[
12z - 42z = -30z
\]

Combine \(48\) and \(-3\):

\[
48 - 3 = 45
\]

So the expression simplifies to:

\[
-30z + 45
\]

3. To express this in fractional form, we can factor out the common factor, if necessary:

\[
-30z + 45 = -15(2z - 3)
\]

Thus, the final answer as a fraction is:

\[
-15(2z - 3)
\]

Alternatively, you can express this in terms of fractions if needed:

\[
-30z + 45 = \frac{-30z + 45}{1}
\]

So, the simplified expression is:

\[
-30z + 45
\] or \(-15(2z - 3)\).