Question

Which expressions are equivalent to -9 (2/3x + 1) Check the two that apply.
(2 points)
• -6x - 9
0-9 (2/3x) - 9(1)
* -6x + 9
* -9 (2/3x) + 9 (1)
* -6x + 1

Answer 1

To determine which expressions are equivalent to \(-9 \left(\frac{2}{3}x + 1\right)\), we need to simplify the expression:

\[
-9 \left(\frac{2}{3}x + 1\right) = -9 \cdot \frac{2}{3}x - 9 \cdot 1
\]
This simplifies to:
\[
-9 \cdot \frac{2}{3}x - 9 = -6x - 9
\]

Now let's evaluate the options given:

1. **-6x - 9**: This is equivalent to our simplified expression, so this is correct.

2. **0 - 9 \left(\frac{2}{3}x\right) - 9(1)**: This simplifies to \(-9 \cdot \frac{2}{3}x - 9\), which is equivalent to \(-6x - 9\). So this also applies.

3. **-6x + 9**: This is not equivalent, as it does not match \(-6x - 9\).

4. **-9 \left(\frac{2}{3}x\right) + 9(1)**: This simplifies to \(-9 \cdot \frac{2}{3}x + 9\), which is \(-6x + 9\), and this is also not equivalent.

5. **-6x + 1**: This is also not equivalent, as it does not match \(-6x - 9\).

Thus, the two expressions that are equivalent to \(-9 \left(\frac{2}{3}x + 1\right)\) are:

- **-6x - 9**
- **0 - 9 (2/3x) - 9(1)**