Question

Which expressions are equivalent to%C2%A0 −9(23x+1) ? Check the%C2%A0two that apply.(2 points) Responses −9(23x)−9(1) negative 9 times open paren 2 thirds x close paren minus 9 times 1 −6x+9 negative 6 x plus 9 −9(23x)+9(1) negative 9 times open paren 2 thirds x close paren plus 9 times 1 −6x−9 negative 6 x minus 9 −6x+1

Answer 1

Let's simplify the expression \(-9(23x + 1)\):

First, apply the distributive property:
\[
-9(23x) - 9(1) = -207x - 9
\]

Now let's check the provided responses to find equivalent expressions:

1. **\(-9(23x) - 9(1)\)**: This is equivalent to \(-207x - 9\), so this is correct.

2. **\(-9(2/3x) - 9\)**: This would result in \(-6x - 9\) since \(-9(2/3) = -6\). Not equivalent.

3. **\(-6x + 9\)**: This is not equivalent to \(-207x - 9\).

4. **\(-9(23x) + 9(1)\)**: This simplifies to \(-207x + 9\), so this is not correct.

5. **\(-6x - 9\)**: This results from \(-9(2/3x) - 9\), resulting in \(-6x - 9\). Not equivalent.

6. **\(-6x + 1\)**: This is not equivalent.

So, out of these options, the two that apply, which are equivalent to \(-9(23x + 1)\) are:

1. \(-9(23x) - 9(1)\)
2. None of the other expressions match \(-207x - 9\).

Thus the only correct response is the first option:
- \(-9(23x) - 9(1)\) is equivalent to the expression \(-9(23x + 1)\).

Unfortunately, it seems that there is only one expression that is equivalent from the provided options.