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]

To find which expressions are equivalent to [tex]$-9\left(\frac{2}{3} x + 1\right)$[/tex], we need to distribute [tex]$-9$[/tex] to both terms inside the parentheses. Let's go through this step-by-step:

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

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

2. Distribute [tex]$-9$[/tex] to [tex]$1$[/tex]:

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

Putting these together, the expression simplifies to:

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

Now we can compare this expression [tex]$-6x - 9$[/tex] with the given options:

1. [tex]$-9\left(\frac{2}{3} x\right) + 9(1)$[/tex]:\
This simplifies to [tex]$-6x + 9$[/tex], which is not equivalent.

2. [tex]$-9\left(\frac{2}{3} x\right) - 9(1)$[/tex]:\
This simplifies to [tex]$-6x - 9$[/tex], which is equivalent.

3. [tex]$-9\left(\frac{2}{3} x\right) + 1$[/tex]:\
This simplifies to [tex]$-6x + 1$[/tex], which is not equivalent.

4. [tex]$-6x + 1$[/tex]:\
This is not equivalent.

5. [tex]$-6x + 9$[/tex]:\
This is not equivalent.

6. [tex]$-6x - 9$[/tex]:\
This is equivalent.

Therefore, the expressions that are equivalent to [tex]$-9\left(\frac{2}{3} x + 1\right)$[/tex] are:
- [tex]$-9\left(\frac{2}{3} x\right) - 9(1)$[/tex]
- [tex]$-6x - 9$[/tex]

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]

Answer :

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