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Answer :
To determine which of the given expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], let's look at each one and compare it carefully to the original expression. We need to find expressions that have the same terms and structure.
1. [tex]\(9x + 6 + 9\)[/tex]:
- Comparing: We see [tex]\(9x\)[/tex], [tex]\(6\)[/tex], and [tex]\(9\)[/tex] as the terms. This doesn't match the original, which has [tex]\(8.9x\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7\)[/tex]. Therefore, this expression is not equivalent.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- Comparing: The terms are [tex]\(8.9\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7x\)[/tex]. The structure doesn't directly match [tex]\(8.9x + 6.2 + 8.7\)[/tex] in terms of order, but the terms themselves are the same, just reordered. This means it is equivalent due to the commutative property of addition.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- Comparing: This expression has the same terms as the original, just reordered. Therefore, it is equivalent by the commutative property of addition.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Comparing: This has the same terms, just in a different order than the original expression, making it equivalent.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- Comparing: This expression has no [tex]\(x\)[/tex] term, which the original expression does have. Hence, it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Comparing: This has the same terms, only in a different order. Thus, it is equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- Comparing: Here, [tex]\(6.2x\)[/tex] is not the same as [tex]\(8.9x\)[/tex]. Therefore, it's not equivalent.
The following expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex]:
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
1. [tex]\(9x + 6 + 9\)[/tex]:
- Comparing: We see [tex]\(9x\)[/tex], [tex]\(6\)[/tex], and [tex]\(9\)[/tex] as the terms. This doesn't match the original, which has [tex]\(8.9x\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7\)[/tex]. Therefore, this expression is not equivalent.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- Comparing: The terms are [tex]\(8.9\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7x\)[/tex]. The structure doesn't directly match [tex]\(8.9x + 6.2 + 8.7\)[/tex] in terms of order, but the terms themselves are the same, just reordered. This means it is equivalent due to the commutative property of addition.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- Comparing: This expression has the same terms as the original, just reordered. Therefore, it is equivalent by the commutative property of addition.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Comparing: This has the same terms, just in a different order than the original expression, making it equivalent.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- Comparing: This expression has no [tex]\(x\)[/tex] term, which the original expression does have. Hence, it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Comparing: This has the same terms, only in a different order. Thus, it is equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- Comparing: Here, [tex]\(6.2x\)[/tex] is not the same as [tex]\(8.9x\)[/tex]. Therefore, it's not equivalent.
The following expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex]:
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- [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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