Answer :
To determine which expressions are equivalent to the original expression [tex]\(8.9x + 6.2 + 8.7\)[/tex], we can examine each expression to see if it rearranges the terms without changing the structure of the expression. The equivalent expressions should have the same coefficient for [tex]\(x\)[/tex] and the same constant term (sum of the constants):
1. [tex]\(9x + 6 + 9\)[/tex]
This expression is not equivalent because the coefficients and constant terms are different from the original expression.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
This expression rearranges the terms but changes how they are related. In the original, [tex]\(x\)[/tex] is with 8.9, but here it is with 8.7, so this is not equivalent.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]
This expression is equivalent to the original as it simply rearranges the terms without changing their values or how they are connected to [tex]\(x\)[/tex].
4. [tex]\(87 + 8.9x + 6.2\)[/tex]
This is not equivalent because the constant term [tex]\(87\)[/tex] significantly changes the value compared to 6.2 and 8.7 from the original expression.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]
This expression does not include the variable [tex]\(x\)[/tex], so it is not equivalent to the original expression.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
This expression rearranges the terms in such a way that it maintains the equivalent structure of the original [tex]\(8.9x + (6.2 + 8.7)\)[/tex]. So it is equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]
This expression changes the variable’s coefficient, attaching it to 6.2 instead of 8.9, making it not equivalent.
From the analysis, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
These options keep the terms represented similarly to the original expression.
1. [tex]\(9x + 6 + 9\)[/tex]
This expression is not equivalent because the coefficients and constant terms are different from the original expression.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
This expression rearranges the terms but changes how they are related. In the original, [tex]\(x\)[/tex] is with 8.9, but here it is with 8.7, so this is not equivalent.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]
This expression is equivalent to the original as it simply rearranges the terms without changing their values or how they are connected to [tex]\(x\)[/tex].
4. [tex]\(87 + 8.9x + 6.2\)[/tex]
This is not equivalent because the constant term [tex]\(87\)[/tex] significantly changes the value compared to 6.2 and 8.7 from the original expression.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]
This expression does not include the variable [tex]\(x\)[/tex], so it is not equivalent to the original expression.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
This expression rearranges the terms in such a way that it maintains the equivalent structure of the original [tex]\(8.9x + (6.2 + 8.7)\)[/tex]. So it is equivalent.
7. [tex]\(8.9 + 6.2x + 8.7\)[/tex]
This expression changes the variable’s coefficient, attaching it to 6.2 instead of 8.9, making it not equivalent.
From the analysis, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
These options keep the terms represented similarly to the original expression.
