Which expressions are equivalent to −9(23x+1)

Question

? Check the two that apply.(2 points)
Responses

−6x+9
negative 6 x plus 9

−9(23x)−9(1)
negative 9 times open paren 2 thirds x close paren minus 9 times 1

−6x+1
negative 6 x plus 1

−6x−9
negative 6 x minus 9

−9(23x)+9(1)

Answer 1

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 \(-207x - 9\).

1. −6x + 9: Not equivalent
2. −9(23x) − 9(1): Equivalent (this simplifies to \(-207x - 9\))
3. −6x + 1: Not equivalent
4. −6x − 9: Not equivalent
5. −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.