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

To simplify the expression \( 12(z + 4) - 3(14z + 1) \), let's follow the steps carefully:

1. **Distribute** the terms inside the parentheses:
\[
12(z + 4) = 12z + 48
\]
\[
-3(14z + 1) = -42z - 3
\]

2. **Combine these results**:
\[
12z + 48 - 42z - 3
\]

3. **Combine like terms**:
- For the \(z\) terms:
\[
12z - 42z = -30z
\]
- For the constant terms:
\[
48 - 3 = 45
\]

4. **Putting it all together**:
\[
-30z + 45
\]

Thus, the simplified expression is:
\[
-30z + 45
\]

If you need to express it in fractional form, you could rewrite it as:
\[
-30z + \frac{45}{1}
\]
But in this case, keeping it as \( -30z + 45 \) is acceptable and clear.

So, the final answer is:
\[
-30z + 45
\]