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Answer :
To find the expressions equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we can consider the order of the terms and focus on the relationships between these terms. The goal is to identify expressions that rearrange these terms but still equal the original expression.
Let's look at each option to determine equivalency with the original expression:
1. [tex]\(9x + 6 + 9\)[/tex]: This expression changes the coefficients and constants, so it is not equivalent.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]: This expression changes the placement of [tex]\(x\)[/tex], as the coefficient 8.9 should be with [tex]\(x\)[/tex], so it is not equivalent.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]: This expression only rearranges the constant terms, which does not affect equivalency. It is equivalent to the original expression.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: This expression reorders the terms, but [tex]\(8.9x\)[/tex] is still present with the same coefficient, making it equivalent to the original expression.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]: This expression lacks the variable [tex]\(x\)[/tex] and changes the structure of the original expression, so it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]: This expression reorders the terms, maintaining the same terms as the original expression, making it equivalent.
7. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: Again, this expression is just a rearrangement of the terms from the original expression, so it is equivalent.
Therefore, the expressions that are 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]
When rearranging terms, as long as the coefficients for corresponding variables stay the same, and constants are preserved in any order, the expressions are equivalent.
Let's look at each option to determine equivalency with the original expression:
1. [tex]\(9x + 6 + 9\)[/tex]: This expression changes the coefficients and constants, so it is not equivalent.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]: This expression changes the placement of [tex]\(x\)[/tex], as the coefficient 8.9 should be with [tex]\(x\)[/tex], so it is not equivalent.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]: This expression only rearranges the constant terms, which does not affect equivalency. It is equivalent to the original expression.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: This expression reorders the terms, but [tex]\(8.9x\)[/tex] is still present with the same coefficient, making it equivalent to the original expression.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]: This expression lacks the variable [tex]\(x\)[/tex] and changes the structure of the original expression, so it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]: This expression reorders the terms, maintaining the same terms as the original expression, making it equivalent.
7. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: Again, this expression is just a rearrangement of the terms from the original expression, so it is equivalent.
Therefore, the expressions that are 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]
When rearranging terms, as long as the coefficients for corresponding variables stay the same, and constants are preserved in any order, the expressions are equivalent.
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