Question

Which expressions are equivalent to −9(2 over 3x+1)
? Check the two that apply.(2 points)
Responses

−6x+9
negative 6 x plus 9

−6x+1
negative 6 x plus 1

−6x−9
negative 6 x minus 9

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

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

Answer 1

are you sure bout that?

Answer 2

To find expressions equivalent to \( -9\left(\frac{2}{3}x + 1\right) \), we can distribute \( -9 \) through the expression:

\[
-9\left(\frac{2}{3}x + 1\right) = -9\left(\frac{2}{3}x\right) - 9(1)
\]

Calculating \( -9\left(\frac{2}{3}x\right) \):

\[
-9\left(\frac{2}{3}x\right) = -\frac{18}{3}x = -6x
\]

And calculating \( -9(1) \):

\[
-9(1) = -9
\]

Putting it all together, we have:

\[
-9\left(\frac{2}{3}x + 1\right) = -6x - 9
\]

Now, checking the response options:

1. \( -6x + 9 \) - **Not Equivalent**
2. \( -6x + 1 \) - **Not Equivalent**
3. \( -6x - 9 \) - **Equivalent**
4. \( -9(23x) - 9(1) \) - **Not Equivalent**, since it contains a mistake in the notation of \( \frac{2}{3} \).
5. \( -9(23x) + 9(1) \) - **Not Equivalent**, for the same reason as above.

Thus, the only equivalent expression is:

- \( -6x - 9 \)

The one that applies is:

- \( -6x - 9 \)

Answer 3

Let’s carefully review the problem to ensure accuracy in identifying equivalent expressions to \( -9\left(\frac{2}{3}x + 1\right) \).

Starting with the expression:

\[
-9\left(\frac{2}{3}x + 1\right)
\]

We can distribute \( -9 \):

\[
-9\left(\frac{2}{3}x\right) + (-9)(1) = -9 \cdot \frac{2}{3}x - 9
\]

Calculating \( -9 \cdot \frac{2}{3}x \):

\[
-9 \cdot \frac{2}{3} = -\frac{18}{3} = -6
\]

Thus:

\[
-9\left(\frac{2}{3}x + 1\right) = -6x - 9
\]

Now, let’s examine the choices provided:

1. \( -6x + 9 \) - Not equivalent
2. \( -6x + 1 \) - Not equivalent
3. \( -6x - 9 \) - **Equivalent**
4. \( -9(2/3x) - 9(1) \) - Correctly written as \( -9 \cdot \frac{2}{3}x - 9 \), which simplifies to \( -6x - 9 \) - **Equivalent**
5. \( -9(2/3x) + 9(1) \) - Would simplify to \( -6x + 9 \) - Not equivalent

So the two equivalent expressions are:

- **\( -6x - 9 \)**
- **The one resembling \( -9\left(\frac{2}{3}x\right) - 9 \)** (if correctly noted as \( -9\left(\frac{2}{3}x\right) - 9 \) rather than \( -9(2/3x) \pm 9(1) \)).

If you were referring to the exact notation in choice 4, it needs to be corrected to present equivalently as stated.

In summary, the confirmed equivalent expressions are:

- \( -6x - 9 \)
- The distribution breakdown of \( -9\left(\frac{2}{3}x\right) - 9(1) = -6x - 9 \) if specified clearly.

Let me know if you need any further clarification!