Answer :
To solve the question of which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to understand that equivalent expressions have the same terms when simplified, regardless of their order. Let's evaluate each option to see if they can be rearranged or simplified to match the original expression.
1. [tex]\(9x + 6 + 9\)[/tex]:
- This expression has different numerical coefficients and constants. It does not match the original expression and cannot be rearranged to do so.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- The expression here changes the order of terms. The original is [tex]\(8.9x + 6.2 + 8.7\)[/tex]. If we rearrange [tex]\(8.9 + 6.2 + 8.7x\)[/tex], it becomes [tex]\(8.7x + 8.9 + 6.2\)[/tex], which does not match.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- This expression is simply a reordering of the original expression's terms. Both have [tex]\(8.9x\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7\)[/tex], so they are equivalent.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Reordering the original expression [tex]\(8.9x + 6.2 + 8.7\)[/tex] to [tex]\(8.7 + 8.9x + 6.2\)[/tex] gives the same terms, making it equivalent.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- This expression has constants but lacks the [tex]\(x\)[/tex] term. It is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Rearranging to [tex]\(8.9x + 6.2 + 8.7\)[/tex] matches the original expression, making it equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- This expression has a different term [tex]\(6.2x\)[/tex] instead of [tex]\(8.9x\)[/tex], making it not equivalent.
Therefore, the expressions 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]
1. [tex]\(9x + 6 + 9\)[/tex]:
- This expression has different numerical coefficients and constants. It does not match the original expression and cannot be rearranged to do so.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- The expression here changes the order of terms. The original is [tex]\(8.9x + 6.2 + 8.7\)[/tex]. If we rearrange [tex]\(8.9 + 6.2 + 8.7x\)[/tex], it becomes [tex]\(8.7x + 8.9 + 6.2\)[/tex], which does not match.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- This expression is simply a reordering of the original expression's terms. Both have [tex]\(8.9x\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7\)[/tex], so they are equivalent.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Reordering the original expression [tex]\(8.9x + 6.2 + 8.7\)[/tex] to [tex]\(8.7 + 8.9x + 6.2\)[/tex] gives the same terms, making it equivalent.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- This expression has constants but lacks the [tex]\(x\)[/tex] term. It is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Rearranging to [tex]\(8.9x + 6.2 + 8.7\)[/tex] matches the original expression, making it equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- This expression has a different term [tex]\(6.2x\)[/tex] instead of [tex]\(8.9x\)[/tex], making it not equivalent.
Therefore, the expressions 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]
