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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 rearrange and check each option to see if they can be rewritten in the same form. Let's break down each choice and see which ones match the original expression.

The original expression is:
[tex]\[ 8.9x + 6.2 + 8.7 \][/tex]

First, we can combine the constant terms in the expression:
[tex]\[ 6.2 + 8.7 = 14.9 \][/tex]

So, the simplified form of the original expression is:
[tex]\[ 8.9x + 14.9 \][/tex]

Now, let's analyze each given option:

1. [tex]\(9x + 6 + 9\)[/tex]
- Simplify the constants: [tex]\(6 + 9 = 15\)[/tex]
- This gives [tex]\(9x + 15\)[/tex], which is not equivalent to [tex]\(8.9x + 14.9\)[/tex].

2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- Rearrange as [tex]\(8.7x + 8.9 + 6.2\)[/tex]
- Simplify the constants: [tex]\(8.9 + 6.2 = 15.1\)[/tex], which does not match [tex]\(8.9x + 14.9\)[/tex].

3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- Rearranging gives [tex]\(8.9x + (8.7 + 6.2)\)[/tex]
- Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex]
- This matches the original expression [tex]\(8.9x + 14.9\)[/tex].

4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- Rearrange as [tex]\(8.9x + (8.7 + 6.2)\)[/tex]
- Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex]
- This also matches the original expression [tex]\(8.9x + 14.9\)[/tex].

5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- Simplify the constants: [tex]\(6.2 + 8.7 + 8.9 = 23.8\)[/tex]
- There is no [tex]\(x\)[/tex] term, so it cannot be equivalent.

6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
- Rearrange as [tex]\(8.9x + (6.2 + 8.7)\)[/tex]
- Simplify the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex]
- This also matches the original expression [tex]\(8.9x + 14.9\)[/tex].

7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]
- This arranges to [tex]\(6.2x + (8.9 + 8.7)\)[/tex] which is [tex]\(6.2x + 17.6\)[/tex]
- This does not match [tex]\(8.9x + 14.9\)[/tex].

Therefore, 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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