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Answer :
To find which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to rearrange or simplify each expression to see if it matches the original expression.
Let's look at the options one by one:
1. [tex]\(9x + 6 + 9\)[/tex]:
- This expression is different. The coefficients and constant terms do not match [tex]\(8.9x + 6.2 + 8.7\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- This expression has terms rearranged, but not correctly grouped. The 'x' is with the wrong term; hence, it’s not equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex].
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- This is equivalent because it simply reorders the terms. Reordering addition doesn't change the result.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- This expression is also equivalent because it includes the same numbers and puts [tex]\(8.9x\)[/tex] in the middle, which is fine due to the commutative property of addition.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- This expression doesn't have the variable 'x' associated with the 8.9, so it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- This expression is equivalent because it includes all the correct terms and is simply in a different order.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- This expression incorrectly applies 'x' to the [tex]\(6.2\)[/tex], altering the meaning of the expression and making it not equivalent.
Therefore, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] by rearranging terms 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]
These equivalent expressions reflect the same mathematical relationship with different orders of addition.
Let's look at the options one by one:
1. [tex]\(9x + 6 + 9\)[/tex]:
- This expression is different. The coefficients and constant terms do not match [tex]\(8.9x + 6.2 + 8.7\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- This expression has terms rearranged, but not correctly grouped. The 'x' is with the wrong term; hence, it’s not equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex].
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- This is equivalent because it simply reorders the terms. Reordering addition doesn't change the result.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- This expression is also equivalent because it includes the same numbers and puts [tex]\(8.9x\)[/tex] in the middle, which is fine due to the commutative property of addition.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- This expression doesn't have the variable 'x' associated with the 8.9, so it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- This expression is equivalent because it includes all the correct terms and is simply in a different order.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- This expression incorrectly applies 'x' to the [tex]\(6.2\)[/tex], altering the meaning of the expression and making it not equivalent.
Therefore, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] by rearranging terms 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]
These equivalent expressions reflect the same mathematical relationship with different orders of addition.
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