Question

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