Question

Add: 12(x+4)+14(4x−2)
1
2
(
𝑥
+
4
)
+
1
4
(
4
𝑥
−
2
)
. Answer should be in mixed number form.(1 point)

Answer 1

To solve the expression \( 12(x+4) + 14(4x−2) \), let's first distribute both terms:

1. Distribute \( 12 \) in \( 12(x+4) \):
\[
12(x) + 12(4) = 12x + 48
\]

2. Distribute \( 14 \) in \( 14(4x−2) \):
\[
14(4x) + 14(-2) = 56x - 28
\]

Now combine the two results:
\[
12x + 48 + 56x - 28
\]

Now, combine the like terms:
- Combine \( 12x \) and \( 56x \):
\[
12x + 56x = 68x
\]

- Combine \( 48 \) and \( -28 \):
\[
48 - 28 = 20
\]

So we have:
\[
68x + 20
\]

Next, we can express this in mixed number form. Since \( 20 \) can be written as \( 20/1 \), we can also express \( 68x + 20 \) as:
\[
68x + 20 = 68x + \frac{20}{1}
\]

This isn't needed in mixed number form. If you want to express \( 20 \) as a mixed number, it would just remain \( 20 \) since it is a whole number.

Therefore, the final answer is:
\[
68x + 20
\]

If you need it in terms of x, we can finalize:
Mixed number form: \( 68x + 20 \).