Answer :
We start by simplifying the original expression:
[tex]$$
8.9x + 6.2 + 8.7.
$$[/tex]
Since [tex]$6.2 + 8.7 = 14.9$[/tex], the simplified expression is
[tex]$$
8.9x + 14.9.
$$[/tex]
Now, we will simplify each candidate expression and compare them with the simplified expression [tex]$8.9x + 14.9$[/tex].
1. Candidate 1:
Expression:
[tex]$$
9x + 6 + 9.
$$[/tex]
Combine the constant terms: [tex]$6 + 9 = 15$[/tex]. Thus,
[tex]$$
9x + 15.
$$[/tex]
This is different from [tex]$8.9x + 14.9$[/tex], so it is not equivalent.
2. Candidate 2:
Expression:
[tex]$$
8.9 + 6.2 + 8.7x.
$$[/tex]
Combine the constant terms: [tex]$8.9 + 6.2 = 15.1$[/tex]. Thus, the expression becomes
[tex]$$
8.7x + 15.1.
$$[/tex]
Again, the coefficient of [tex]$x$[/tex] and the constant term differ from [tex]$8.9x + 14.9$[/tex], so it is not equivalent.
3. Candidate 3:
Expression:
[tex]$$
8.9x + 8.7 + 6.2.
$$[/tex]
Here, [tex]$8.7 + 6.2 = 14.9$[/tex], so the expression simplifies to
[tex]$$
8.9x + 14.9.
$$[/tex]
This is exactly the same as the original simplified expression.
4. Candidate 4:
Expression:
[tex]$$
8.7 + 8.9x + 6.2.
$$[/tex]
The order of addition does not affect the result. Grouping the constant terms:
[tex]$$
8.7 + 6.2 = 14.9.
$$[/tex]
The expression becomes
[tex]$$
8.9x + 14.9,
$$[/tex]
which is equivalent to the original expression.
5. Candidate 5:
Expression:
[tex]$$
6.2 + 8.7 + 8.9.
$$[/tex]
This expression contains only constants. Adding them, we get
[tex]$$
6.2 + 8.7 + 8.9 = 23.8.
$$[/tex]
Since there is no [tex]$x$[/tex] term, it is not equivalent.
6. Candidate 6:
Expression:
[tex]$$
6.2 + 8.7 + 8.9x.
$$[/tex]
Again, combine the constants: [tex]$6.2 + 8.7 = 14.9$[/tex]. Thus, the expression becomes
[tex]$$
8.9x + 14.9,
$$[/tex]
which is equivalent.
7. Candidate 7:
Expression:
[tex]$$
8.9 + 6.2x + 8.7.
$$[/tex]
Combine [tex]$8.9 + 8.7 = 17.6$[/tex], so the expression is
[tex]$$
6.2x + 17.6.
$$[/tex]
This does not match [tex]$8.9x + 14.9$[/tex], so it is not equivalent.
After comparing all candidates, we see that the expressions equivalent to the original are those that simplify to
[tex]$$
8.9x + 14.9.
$$[/tex]
Thus, the expressions corresponding to Candidate 3, Candidate 4, and Candidate 6 are equivalent to the original expression.
[tex]$$
8.9x + 6.2 + 8.7.
$$[/tex]
Since [tex]$6.2 + 8.7 = 14.9$[/tex], the simplified expression is
[tex]$$
8.9x + 14.9.
$$[/tex]
Now, we will simplify each candidate expression and compare them with the simplified expression [tex]$8.9x + 14.9$[/tex].
1. Candidate 1:
Expression:
[tex]$$
9x + 6 + 9.
$$[/tex]
Combine the constant terms: [tex]$6 + 9 = 15$[/tex]. Thus,
[tex]$$
9x + 15.
$$[/tex]
This is different from [tex]$8.9x + 14.9$[/tex], so it is not equivalent.
2. Candidate 2:
Expression:
[tex]$$
8.9 + 6.2 + 8.7x.
$$[/tex]
Combine the constant terms: [tex]$8.9 + 6.2 = 15.1$[/tex]. Thus, the expression becomes
[tex]$$
8.7x + 15.1.
$$[/tex]
Again, the coefficient of [tex]$x$[/tex] and the constant term differ from [tex]$8.9x + 14.9$[/tex], so it is not equivalent.
3. Candidate 3:
Expression:
[tex]$$
8.9x + 8.7 + 6.2.
$$[/tex]
Here, [tex]$8.7 + 6.2 = 14.9$[/tex], so the expression simplifies to
[tex]$$
8.9x + 14.9.
$$[/tex]
This is exactly the same as the original simplified expression.
4. Candidate 4:
Expression:
[tex]$$
8.7 + 8.9x + 6.2.
$$[/tex]
The order of addition does not affect the result. Grouping the constant terms:
[tex]$$
8.7 + 6.2 = 14.9.
$$[/tex]
The expression becomes
[tex]$$
8.9x + 14.9,
$$[/tex]
which is equivalent to the original expression.
5. Candidate 5:
Expression:
[tex]$$
6.2 + 8.7 + 8.9.
$$[/tex]
This expression contains only constants. Adding them, we get
[tex]$$
6.2 + 8.7 + 8.9 = 23.8.
$$[/tex]
Since there is no [tex]$x$[/tex] term, it is not equivalent.
6. Candidate 6:
Expression:
[tex]$$
6.2 + 8.7 + 8.9x.
$$[/tex]
Again, combine the constants: [tex]$6.2 + 8.7 = 14.9$[/tex]. Thus, the expression becomes
[tex]$$
8.9x + 14.9,
$$[/tex]
which is equivalent.
7. Candidate 7:
Expression:
[tex]$$
8.9 + 6.2x + 8.7.
$$[/tex]
Combine [tex]$8.9 + 8.7 = 17.6$[/tex], so the expression is
[tex]$$
6.2x + 17.6.
$$[/tex]
This does not match [tex]$8.9x + 14.9$[/tex], so it is not equivalent.
After comparing all candidates, we see that the expressions equivalent to the original are those that simplify to
[tex]$$
8.9x + 14.9.
$$[/tex]
Thus, the expressions corresponding to Candidate 3, Candidate 4, and Candidate 6 are equivalent to the original expression.
