Which expressions are equivalent to [tex]-9\left(\frac{2}{3} x+1\right)[/tex]? Check all that apply.

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

B. [tex]-9\left(\frac{2}{3} x\right)-9(1)[/tex]

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

D. [tex]-6 x+1[/tex]

E. [tex]-6 x+9[/tex]

F. [tex]-6 x-9[/tex]

Let's break down the original expression and find which of the given expressions are equivalent to it.

The original expression is:

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

To simplify, we need to distribute the [tex]\(-9\)[/tex] through the parentheses:

1. Distribute [tex]\(-9\)[/tex] to [tex]\(\frac{2}{3}x\)[/tex]:

[tex]\(-9 \times \frac{2}{3}x = -6x\)[/tex]

2. Distribute [tex]\(-9\)[/tex] to [tex]\(1\)[/tex]:

[tex]\(-9 \times 1 = -9\)[/tex]

Putting it all together, the simplified expression is:

[tex]\[ -6x - 9 \][/tex]

Now, let's compare the given expressions to [tex]\(-6x - 9\)[/tex] to see which ones are equivalent:

1. [tex]\(-9\left(\frac{2}{3} x\right) + 9(1)\)[/tex] simplifies to [tex]\(-6x + 9\)[/tex]

2. [tex]\(-9\left(\frac{2}{3} x\right) - 9(1)\)[/tex] simplifies to [tex]\(-6x - 9\)[/tex]

3. [tex]\(-9\left(\frac{2}{3} x\right) + 1\)[/tex] simplifies to [tex]\(-6x + 1\)[/tex]

4. [tex]\(-6x + 1\)[/tex]

5. [tex]\(-6x + 9\)[/tex]

6. [tex]\(-6x - 9\)[/tex]

The expressions that are equivalent to the original expression [tex]\(-6x - 9\)[/tex] are:

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

So, the correct choices are the second and sixth expressions.

Which expressions are equivalent to [tex]-9\left(\frac{2}{3} x+1\right)[/tex]? Check all that apply.A. [tex]-9\left(\frac{2}{3} x\right)+9(1)[/tex]B. [tex]-9\left(\frac{2}{3} x\right)-9(1)[/tex]C. [tex]-9\left(\frac{2}{3} x\right)+1[/tex]D. [tex]-6 x+1[/tex]E. [tex]-6 x+9[/tex]F. [tex]-6 x-9[/tex]

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