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 determine which expressions are equivalent to [tex]$-9\left(\frac{2}{3} x+1\right)$[/tex], let's simplify the given expression.

1. Start with the original expression:

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

2. Distribute the [tex]$-9$[/tex] across the terms inside the parentheses:

- Multiply [tex]$-9$[/tex] by [tex]$\frac{2}{3} x$[/tex]:
[tex]\[
-9 \times \frac{2}{3} x = -6x
\][/tex]

- Multiply [tex]$-9$[/tex] by [tex]$1$[/tex]:
[tex]\[
-9 \times 1 = -9
\][/tex]

3. Combine these results into a single expression:

So, the expression becomes:
[tex]\[
-6x - 9
\][/tex]

Now, compare this simplified expression to the options provided:

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

The expression [tex]$-6x - 9$[/tex] matches exactly with the last option given. Therefore, the equivalent expression to the original is:

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

This is the only option among the list that is equivalent to the provided expression after simplification.

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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