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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]$6.9x + 8.7 + 6.2$[/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]$8.9 + 8.2x + 8.7$[/tex]

Answer :

To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to simplify each given expression and compare them to the simplified form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].

First, let's simplify [tex]\(8.9x + 6.2 + 8.7\)[/tex]:
[tex]\[ 8.9x + 6.2 + 8.7 = 8.9x + (6.2 + 8.7) \][/tex]
[tex]\[ = 8.9x + 14.9 \][/tex]

Now, let's simplify each candidate expression one by one and compare it to [tex]\(8.9x + 14.9\)[/tex]:

1. [tex]\(9x + 6 + 9\)[/tex]:
[tex]\[ 9x + 6 + 9 = 9x + 15 \][/tex]
[tex]\[ \neq 8.9x + 14.9 \][/tex]

2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
[tex]\[ 8.9 + 6.2 + 8.7x = (8.9 + 6.2) + 8.7x \][/tex]
[tex]\[ = 15.1 + 8.7x \][/tex]
[tex]\[ \neq 8.9x + 14.9 \][/tex]

3. [tex]\(6.9x + 8.7 + 6.2\)[/tex]:
[tex]\[ 6.9x + 8.7 + 6.2 = 6.9x + (8.7 + 6.2) \][/tex]
[tex]\[ = 6.9x + 14.9 \][/tex]
[tex]\[ \neq 8.9x + 14.9 \][/tex]

4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
[tex]\[ 8.7 + 8.9x + 6.2 = (8.7 + 6.2) + 8.9x \][/tex]
[tex]\[ = 14.9 + 8.9x \][/tex]
[tex]\[ = 8.9x + 14.9 \][/tex]
[tex]\[ = 8.9x + 14.9 \][/tex]
[tex]\[ = 8.9x + 14.9 \][/tex] (This is equivalent)

5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
[tex]\[ 6.2 + 8.7 + 8.9 = (6.2 + 8.7) + 8.9 \][/tex]
[tex]\[ = 14.9 + 8.9 \][/tex]
[tex]\[ = 23.8 \][/tex]
[tex]\[ \neq 8.9x + 14.9 \][/tex]

6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
[tex]\[ 6.2 + 8.7 + 8.9x = (6.2 + 8.7) + 8.9x \][/tex]
[tex]\[ = 14.9 + 8.9x \][/tex]
[tex]\[ = 8.9x + 14.9 \][/tex] (This is equivalent)

7. [tex]\(8.9 + 8.2x + 8.7\)[/tex]:
[tex]\[ 8.9 + 8.2x + 8.7 = (8.9 + 8.7) + 8.2x \][/tex]
[tex]\[ = 17.6 + 8.2x \][/tex]
[tex]\[ \neq 8.9x + 14.9 \][/tex]

From these comparisons, we find that the expressions equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:

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

Therefore, the correct expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:

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

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