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Which expressions are equivalent to [tex]8.9x + 6.2 + 8.7[/tex]? Check all that apply.

A. [tex]9x + 6 + 9[/tex]

B. [tex]8.9 + 6.2 + 8.7x[/tex]

C. [tex]8.9x + 8.7 + 6.2[/tex]

D. [tex]8.7 + 8.9x + 6.2[/tex]

E. [tex]6.2 + 8.7 + 8.9[/tex]

F. [tex]6.2 + 8.7 + 8.9x[/tex]

G. [tex]8.9 + 6.2x + 8.7[/tex]

Answer :

To determine which expressions are equivalent to [tex]\( 8.9x + 6.2 + 8.7 \)[/tex], we need to compare each given expression with this one. Let’s examine them one by one.

### Given Expression and Simplification:
[tex]\[ 8.9x + 6.2 + 8.7 \][/tex]
This can be simplified to:
[tex]\[ 8.9x + (6.2 + 8.7) \][/tex]
[tex]\[ 8.9x + 14.9 \][/tex]

### Check each expression:

1. [tex]\( 9x + 6 + 9 \)[/tex]:
Simplifying:
[tex]\[ 9x + (6 + 9) \][/tex]
[tex]\[ 9x + 15 \][/tex]
This is not equal to [tex]\( 8.9x + 14.9 \)[/tex].

2. [tex]\( 8.9 + 6.2 + 8.7x \)[/tex]:
Simplifying:
[tex]\[ (8.9 + 6.2) + 8.7x \][/tex]
[tex]\[ 15.1 + 8.7x \][/tex]
This is not equal to [tex]\( 8.9x + 14.9 \)[/tex].

3. [tex]\( 8.9x + 8.7 + 6.2 \)[/tex]:
Simplifying:
[tex]\[ 8.9x + (8.7 + 6.2) \][/tex]
[tex]\[ 8.9x + 14.9 \][/tex]
This is equal to [tex]\( 8.9x + 14.9 \)[/tex].

4. [tex]\( 8.7 + 8.9x + 6.2 \)[/tex]:
Simplifying:
[tex]\[ (8.7 + 6.2) + 8.9x \][/tex]
[tex]\[ 14.9 + 8.9x \][/tex]
This is equal to [tex]\( 8.9x + 14.9 \)[/tex].

5. [tex]\( 6.2 + 8.7 + 8.9 \)[/tex]:
Simplifying:
[tex]\[ (6.2 + 8.7 + 8.9) \][/tex]
[tex]\[ 23.8 \][/tex]
This is not equal to [tex]\( 8.9x + 14.9 \)[/tex].

6. [tex]\( 6.2 + 8.7 + 8.9x \)[/tex]:
Simplifying:
[tex]\[ (6.2 + 8.7) + 8.9x \][/tex]
[tex]\[ 14.9 + 8.9x \][/tex]
This is equal to [tex]\( 8.9x + 14.9 \)[/tex].

7. [tex]\( 8.9 + 6.2x + 8.7 \)[/tex]:
Simplifying:
[tex]\[ (8.9 + 8.7) + 6.2x \][/tex]
[tex]\[ 17.6 + 6.2x \][/tex]
This is not equal to [tex]\( 8.9x + 14.9 \)[/tex].

### Conclusion:
The expressions equivalent to [tex]\( 8.9x + 6.2 + 8.7 \)[/tex] are:

- [tex]\( 8.9x + 8.7 + 6.2 \)[/tex]
- [tex]\( 8.7 + 8.9x + 6.2 \)[/tex]
- [tex]\( 6.2 + 8.7 + 8.9x \)[/tex]

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