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Answer :
To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to rewrite or rearrange the terms and see if they match the original expression. Let's go through each option:
1. Option: [tex]\(9x + 6 + 9\)[/tex]:
This expression simplifies to [tex]\(9x + 15\)[/tex]. Since this has different coefficients and constants than [tex]\(8.9x + 6.2 + 8.7\)[/tex], it is not equivalent.
2. Option: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
By rearranging the terms, we have [tex]\(8.7x + 8.9 + 6.2\)[/tex]. This uses the commutative property of addition, making it equivalent to the original expression we are considering.
3. Option: [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
This is exactly the same as the original expression, just with the constant terms rearranged. Therefore, it is clearly equivalent.
4. Option: [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
By rearranging the terms, we have [tex]\(8.9x + 6.2 + 8.7\)[/tex], which is exactly the original expression, so it is equivalent.
5. Option: [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
This simplifies to [tex]\(23.8\)[/tex] and does not contain the [tex]\(x\)[/tex] term, so it is not equivalent to the original expression.
6. Option: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
By rearranging, this expression becomes [tex]\(8.9x + 6.2 + 8.7\)[/tex], which matches the original expression. This means it is equivalent.
7. Option: [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
This expression does not have the [tex]\(x\)[/tex] coefficient applied correctly, making it [tex]\(6.2x + 17.6\)[/tex], thus it is not equivalent to our original expression.
From this analysis, the expressions equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [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. Option: [tex]\(9x + 6 + 9\)[/tex]:
This expression simplifies to [tex]\(9x + 15\)[/tex]. Since this has different coefficients and constants than [tex]\(8.9x + 6.2 + 8.7\)[/tex], it is not equivalent.
2. Option: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
By rearranging the terms, we have [tex]\(8.7x + 8.9 + 6.2\)[/tex]. This uses the commutative property of addition, making it equivalent to the original expression we are considering.
3. Option: [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
This is exactly the same as the original expression, just with the constant terms rearranged. Therefore, it is clearly equivalent.
4. Option: [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
By rearranging the terms, we have [tex]\(8.9x + 6.2 + 8.7\)[/tex], which is exactly the original expression, so it is equivalent.
5. Option: [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
This simplifies to [tex]\(23.8\)[/tex] and does not contain the [tex]\(x\)[/tex] term, so it is not equivalent to the original expression.
6. Option: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
By rearranging, this expression becomes [tex]\(8.9x + 6.2 + 8.7\)[/tex], which matches the original expression. This means it is equivalent.
7. Option: [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
This expression does not have the [tex]\(x\)[/tex] coefficient applied correctly, making it [tex]\(6.2x + 17.6\)[/tex], thus it is not equivalent to our original expression.
From this analysis, the expressions equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [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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