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

Question

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

−6x+1
negative 6 x plus 1

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

−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−9

Answer 1

To determine which expressions are equivalent to \(-9(23x + 1)\), we first need to distribute \(-9\) across the terms inside the parentheses:

\[ -9(23x + 1) = -9 \cdot 23x + (-9) \cdot 1 = -207x - 9 \]

Now let's analyze each of the provided options:

1. \(-6x + 1\): This is not equivalent because \(-207x - 9\) does not equal \(-6x + 1\).

2. \(-9(23x) + 9(1)\): This is incorrect because it simplifies to \(-207x + 9\), which does not match \(-207x - 9\).

3. \(-6x + 9\): This is incorrect because it does not match \(-207x - 9\).

4. \(-9(23x) - 9(1)\): This is equivalent since it would simplify to \(-207x - 9\) (since the negative sign matches, we factor in the distribution correctly).

5. \(-6x - 9\): This is not equivalent because \(-207x - 9\) does not equal \(-6x - 9\).

After this evaluation, the only correct expression that is equivalent to \(-9(23x + 1)\) is:

−9(23x)−9(1).

Therefore, the two options that apply are:

1. \(-9(23x)−9(1)\).
2. None of the others apply.

(Note: It appears there's only one valid option that matches).