Answer :
To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], let's examine each option and compare them to the original expression.
1. Option: [tex]\(9x + 6 + 9\)[/tex]
- This expression is not equivalent because the coefficient of [tex]\(x\)[/tex] and the constants do not match the original expression.
2. Option: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- Rearranging the terms gives you [tex]\(8.7x + 8.9 + 6.2\)[/tex], which is equivalent to the original expression because it has the same parts: [tex]\(8.9x + 6.2 + 8.7\)[/tex].
3. Option: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- This expression just rearranges the constants. It is equivalent to the original expression since it maintains the structure [tex]\(8.9x + (6.2 + 8.7)\)[/tex].
4. Option: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- Again, this expression rearranges the terms. It's equivalent because rearranging terms does not change the overall value when added.
5. Option: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- This expression has no [tex]\(x\)[/tex] term, so it cannot be equivalent to the original expression, which includes a variable term.
6. Option: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
- Rearranging gives [tex]\(8.9x + 6.2 + 8.7\)[/tex], which matches the original expression in structure and values.
7. Option: [tex]\(8.9 + 8.2x + 8.7\)[/tex]
- This expression is not equivalent due to the wrong coefficient for [tex]\(x\)[/tex]. The [tex]\(x\)[/tex] term should have a coefficient of 8.9, not 8.2.
Based on the analysis, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- [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 correspond to options 2, 3, 4, and 6.
1. Option: [tex]\(9x + 6 + 9\)[/tex]
- This expression is not equivalent because the coefficient of [tex]\(x\)[/tex] and the constants do not match the original expression.
2. Option: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- Rearranging the terms gives you [tex]\(8.7x + 8.9 + 6.2\)[/tex], which is equivalent to the original expression because it has the same parts: [tex]\(8.9x + 6.2 + 8.7\)[/tex].
3. Option: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- This expression just rearranges the constants. It is equivalent to the original expression since it maintains the structure [tex]\(8.9x + (6.2 + 8.7)\)[/tex].
4. Option: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- Again, this expression rearranges the terms. It's equivalent because rearranging terms does not change the overall value when added.
5. Option: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- This expression has no [tex]\(x\)[/tex] term, so it cannot be equivalent to the original expression, which includes a variable term.
6. Option: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
- Rearranging gives [tex]\(8.9x + 6.2 + 8.7\)[/tex], which matches the original expression in structure and values.
7. Option: [tex]\(8.9 + 8.2x + 8.7\)[/tex]
- This expression is not equivalent due to the wrong coefficient for [tex]\(x\)[/tex]. The [tex]\(x\)[/tex] term should have a coefficient of 8.9, not 8.2.
Based on the analysis, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- [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 correspond to options 2, 3, 4, and 6.
