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

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

GPT-4o mini · Answer

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.