Answer :
To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to see if the expressions provided have the same structure in terms of coefficients and constants.
Let's analyze each expression:
1. [tex]\(9x + 6 + 9\)[/tex] - This expression is not equivalent because the coefficients and constants are different from [tex]\(8.9x + 6.2 + 8.7\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex] - The structure here is incorrect. The coefficient of [tex]\(x\)[/tex] should be [tex]\(8.9\)[/tex], but it's given as part of the constant terms.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex] - This expression is equivalent to the given one. It has the same terms with just a different order, [tex]\(8.9x + 6.2 + 8.7\)[/tex].
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex] - This expression is equivalent as well. The terms [tex]\(8.9x\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7\)[/tex] are rearranged, but their values remain the same.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex] - This expression is not equivalent because it consists only of constants, lacking the [tex]\(x\)[/tex] term with coefficient [tex]\(8.9\)[/tex].
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex] - This expression is equivalent. The terms are reordered, but it maintains the coefficient of [tex]\(8.9\)[/tex] for [tex]\(x\)[/tex], and the constants are the same.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex] - This does not match because the coefficient of [tex]\(x\)[/tex], [tex]\(6.2\)[/tex], is different from the given expression's [tex]\(8.9\)[/tex].
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]
Let's analyze each expression:
1. [tex]\(9x + 6 + 9\)[/tex] - This expression is not equivalent because the coefficients and constants are different from [tex]\(8.9x + 6.2 + 8.7\)[/tex].
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex] - The structure here is incorrect. The coefficient of [tex]\(x\)[/tex] should be [tex]\(8.9\)[/tex], but it's given as part of the constant terms.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex] - This expression is equivalent to the given one. It has the same terms with just a different order, [tex]\(8.9x + 6.2 + 8.7\)[/tex].
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex] - This expression is equivalent as well. The terms [tex]\(8.9x\)[/tex], [tex]\(6.2\)[/tex], and [tex]\(8.7\)[/tex] are rearranged, but their values remain the same.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex] - This expression is not equivalent because it consists only of constants, lacking the [tex]\(x\)[/tex] term with coefficient [tex]\(8.9\)[/tex].
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex] - This expression is equivalent. The terms are reordered, but it maintains the coefficient of [tex]\(8.9\)[/tex] for [tex]\(x\)[/tex], and the constants are the same.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex] - This does not match because the coefficient of [tex]\(x\)[/tex], [tex]\(6.2\)[/tex], is different from the given expression's [tex]\(8.9\)[/tex].
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]