Question

which two statements are correct when simplifying this expression

12 + 6(3x - 2)

first calculate 6(3x - 2)

first calculate 12 + 6

12 + 6(3x - 2) = 54x - 36

12 + 6(3x - 2) = 18x

12 + 6(3x - 2) = 18x - 24

Answer 1

To simplify the expression \( 12 + 6(3x - 2) \), we need to follow the order of operations.

1. **First, calculate** \( 6(3x - 2) \):
\[
6(3x - 2) = 6 \cdot 3x - 6 \cdot 2 = 18x - 12
\]

2. **Then, add 12** to this result:
\[
12 + (18x - 12) = 18x
\]

Based on the calculations, the correct statements regarding the simplification of the expression are:

1. **First calculate** \( 6(3x - 2) \) (this is true).
2. **12 + 6(3x - 2) = 18x** (this is also true).

Now, let's verify the other statements:

- **First calculate \( 12 + 6 \)**: This is not necessary for simplifying the given expression, so it is incorrect.

- **12 + 6(3x - 2) = 54x - 36**: This is incorrect based on our calculations.

- **12 + 6(3x - 2) = 18x - 24**: This is incorrect as well.

Thus, the two correct statements are:
1. "First calculate \( 6(3x - 2) \)".
2. "12 + 6(3x - 2) = 18x".