Answer :
To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to check if rearranging or grouping the terms results in the same expression. Let's go through each option to see which ones are equivalent:
1. [tex]\(9x + 6 + 9\)[/tex]: This expression changes both the coefficients and the constants, so it is not equivalent.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]: Here, the term involving [tex]\(x\)[/tex] has been moved, but the coefficients of the constants and the [tex]\(x\)[/tex] term differ, so it's not equivalent.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]: This expression simply reorders the addition of constants and the term with [tex]\(x\)[/tex]. Since addition is commutative, this is equivalent to the original expression.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: Similar to option 3, this expression changes the order of terms but remains equivalent to the original due to the commutative property of addition.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]: This expression lacks the [tex]\(x\)[/tex] term, so it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]: Reordering the terms without changing their structure makes this equivalent to the original expression.
7. [tex]\((8.7 + 8.9x) + 6.2\)[/tex]: The order of operations is altered with parentheses, but since they only affect the grouping and not the value, this expression is also equivalent.
Based on the above analysis, 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]
- [tex]\((8.7 + 8.9x) + 6.2\)[/tex]
Thus, the equivalent expressions are options 3, 4, 6, and 7.
1. [tex]\(9x + 6 + 9\)[/tex]: This expression changes both the coefficients and the constants, so it is not equivalent.
2. [tex]\(8.9 + 6.2 + 8.7x\)[/tex]: Here, the term involving [tex]\(x\)[/tex] has been moved, but the coefficients of the constants and the [tex]\(x\)[/tex] term differ, so it's not equivalent.
3. [tex]\(8.9x + 8.7 + 6.2\)[/tex]: This expression simply reorders the addition of constants and the term with [tex]\(x\)[/tex]. Since addition is commutative, this is equivalent to the original expression.
4. [tex]\(8.7 + 8.9x + 6.2\)[/tex]: Similar to option 3, this expression changes the order of terms but remains equivalent to the original due to the commutative property of addition.
5. [tex]\(6.2 + 8.7 + 8.9\)[/tex]: This expression lacks the [tex]\(x\)[/tex] term, so it is not equivalent.
6. [tex]\(6.2 + 8.7 + 8.9x\)[/tex]: Reordering the terms without changing their structure makes this equivalent to the original expression.
7. [tex]\((8.7 + 8.9x) + 6.2\)[/tex]: The order of operations is altered with parentheses, but since they only affect the grouping and not the value, this expression is also equivalent.
Based on the above analysis, 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]
- [tex]\((8.7 + 8.9x) + 6.2\)[/tex]
Thus, the equivalent expressions are options 3, 4, 6, and 7.
