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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

1 answer

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".