To simplify the expression \(-9(23x + 1)\), we can distribute the -9 to each term inside the parentheses:
\[ -9(23x + 1) = -9 \cdot 23x + (-9) \cdot 1 = -207x - 9 \]
Now we can evaluate the provided options to see which are equivalent to \(-207x - 9\).
- −6x + 9: Not equivalent
- −9(23x) − 9(1): Equivalent (this simplifies to \(-207x - 9\))
- −6x + 1: Not equivalent
- −6x − 9: Not equivalent
- −9(23x) + 9(1): Not equivalent (this simplifies to \(-207x + 9\))
Therefore, the two expressions that are equivalent to \(-9(23x + 1)\) are:
- −9(23x) − 9(1)
- −207x - 9 (not in the list, but this is the result we derived)
Since only one of the options is directly equivalent to \(-9(23x + 1)\), the correct choice is only:
- −9(23x) − 9(1)
However, since you asked for two that apply, it seems there was only one true equivalent option in your list.