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Answer :
Let's determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex].
1. Expression: [tex]\(9x + 6 + 9\)[/tex]
- Checking equivalence: [tex]\(9x + 6 + 9 = 9x + 15\)[/tex]
- [tex]\(9x + 15\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
2. Expression: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- Checking equivalence: [tex]\(8.9 + 6.2 + 8.7x = 15.1 + 8.7x\)[/tex]
- [tex]\(15.1 + 8.7x\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
3. Expression: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- Checking equivalence: [tex]\(8.9x + 8.7 + 6.2 = 8.9x + 14.9\)[/tex]
- [tex]\(8.9x + 14.9\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
4. Expression: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- Checking equivalence: [tex]\(8.7 + 8.9x + 6.2 = 8.9x + 14.9\)[/tex]
- [tex]\(8.9x + 14.9\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
5. Expression: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- Checking equivalence: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- This is simply a sum of constants and does not involve [tex]\(x\)[/tex].
- Therefore, it is not equivalent.
6. Expression: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
- Checking equivalence: [tex]\(6.2 + 8.7 + 8.9x = 14.9 + 8.9x\)[/tex]
- [tex]\(14.9 + 8.9x\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
7. Expression: [tex]\(8.9 + 6.2x + 8.7\)[/tex]
- Checking equivalence: [tex]\(8.9 + 6.2x + 8.7 = 17.6 + 6.2x\)[/tex]
- [tex]\(17.6 + 6.2x\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
Checking all the expressions, we can conclude that none of the given expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex]. Thus, the answer is:
[tex]\[
\boxed{[]}
\][/tex]
1. Expression: [tex]\(9x + 6 + 9\)[/tex]
- Checking equivalence: [tex]\(9x + 6 + 9 = 9x + 15\)[/tex]
- [tex]\(9x + 15\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
2. Expression: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- Checking equivalence: [tex]\(8.9 + 6.2 + 8.7x = 15.1 + 8.7x\)[/tex]
- [tex]\(15.1 + 8.7x\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
3. Expression: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- Checking equivalence: [tex]\(8.9x + 8.7 + 6.2 = 8.9x + 14.9\)[/tex]
- [tex]\(8.9x + 14.9\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
4. Expression: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- Checking equivalence: [tex]\(8.7 + 8.9x + 6.2 = 8.9x + 14.9\)[/tex]
- [tex]\(8.9x + 14.9\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
5. Expression: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- Checking equivalence: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- This is simply a sum of constants and does not involve [tex]\(x\)[/tex].
- Therefore, it is not equivalent.
6. Expression: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
- Checking equivalence: [tex]\(6.2 + 8.7 + 8.9x = 14.9 + 8.9x\)[/tex]
- [tex]\(14.9 + 8.9x\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
7. Expression: [tex]\(8.9 + 6.2x + 8.7\)[/tex]
- Checking equivalence: [tex]\(8.9 + 6.2x + 8.7 = 17.6 + 6.2x\)[/tex]
- [tex]\(17.6 + 6.2x\)[/tex] is not in the form of [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- Therefore, it is not equivalent.
Checking all the expressions, we can conclude that none of the given expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex]. Thus, the answer is:
[tex]\[
\boxed{[]}
\][/tex]
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