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Answer :
We start with the original expression:
[tex]$$
8.9x + 6.2 + 8.7.
$$[/tex]
Step 1. Combine the constant terms:
[tex]$$
6.2 + 8.7 = 14.9.
$$[/tex]
So the expression becomes:
[tex]$$
8.9x + 14.9.
$$[/tex]
Step 2. Now, check each option to see if it is equivalent to [tex]$8.9x + 14.9$[/tex].
1. Option 1:
[tex]$$
9x + 6 + 9 = 9x + 15.
$$[/tex]
The coefficient of [tex]$x$[/tex] is [tex]$9$[/tex] (instead of [tex]$8.9$[/tex]) and the constant is [tex]$15$[/tex] (instead of [tex]$14.9$[/tex]). Thus, this option is not equivalent.
2. Option 2:
[tex]$$
8.9 + 6.2 + 8.7x.
$$[/tex]
Here, the term with [tex]$x$[/tex] is [tex]$8.7x$[/tex] and the constant is [tex]$8.9 + 6.2 = 15.1$[/tex]. Both parts do not match the original expression. Therefore, this option is not equivalent.
3. Option 3:
[tex]$$
8.9x + 8.7 + 6.2.
$$[/tex]
The constant part is:
[tex]$$
8.7 + 6.2 = 14.9,
$$[/tex]
and the [tex]$x$[/tex]-term is [tex]$8.9x$[/tex]. This exactly matches the original expression.
4. Option 4:
[tex]$$
8.7 + 8.9x + 6.2.
$$[/tex]
Rearranging the terms, we still have:
[tex]$$
8.9x + (8.7 + 6.2) = 8.9x + 14.9,
$$[/tex]
which is equivalent to the original expression.
5. Option 5:
[tex]$$
6.2 + 8.7 + 8.9.
$$[/tex]
This option has only constant terms (it does not include an [tex]$x$[/tex] term) and sums to [tex]$6.2 + 8.7 + 8.9 = 23.8$[/tex], so it is not equivalent.
6. Option 6:
[tex]$$
6.2 + 87 + 89x.
$$[/tex]
Here, the [tex]$x$[/tex]-term is [tex]$89x$[/tex] and the constant is [tex]$6.2 + 87 = 93.2$[/tex], which does not match the original expression.
7. Option 7:
[tex]$$
8.9 + 62x + 87.
$$[/tex]
In this option, the variable term is [tex]$62x$[/tex] and the constant is [tex]$8.9 + 87 = 95.9$[/tex]. This also does not match the original expression.
Conclusion: Only Options 3 and 4 simplify to
[tex]$$
8.9x + 14.9,
$$[/tex]
which means they are equivalent to the original expression.
Thus, the expressions equivalent to [tex]$8.9x+6.2+8.7$[/tex] are Options 3 and 4.
[tex]$$
8.9x + 6.2 + 8.7.
$$[/tex]
Step 1. Combine the constant terms:
[tex]$$
6.2 + 8.7 = 14.9.
$$[/tex]
So the expression becomes:
[tex]$$
8.9x + 14.9.
$$[/tex]
Step 2. Now, check each option to see if it is equivalent to [tex]$8.9x + 14.9$[/tex].
1. Option 1:
[tex]$$
9x + 6 + 9 = 9x + 15.
$$[/tex]
The coefficient of [tex]$x$[/tex] is [tex]$9$[/tex] (instead of [tex]$8.9$[/tex]) and the constant is [tex]$15$[/tex] (instead of [tex]$14.9$[/tex]). Thus, this option is not equivalent.
2. Option 2:
[tex]$$
8.9 + 6.2 + 8.7x.
$$[/tex]
Here, the term with [tex]$x$[/tex] is [tex]$8.7x$[/tex] and the constant is [tex]$8.9 + 6.2 = 15.1$[/tex]. Both parts do not match the original expression. Therefore, this option is not equivalent.
3. Option 3:
[tex]$$
8.9x + 8.7 + 6.2.
$$[/tex]
The constant part is:
[tex]$$
8.7 + 6.2 = 14.9,
$$[/tex]
and the [tex]$x$[/tex]-term is [tex]$8.9x$[/tex]. This exactly matches the original expression.
4. Option 4:
[tex]$$
8.7 + 8.9x + 6.2.
$$[/tex]
Rearranging the terms, we still have:
[tex]$$
8.9x + (8.7 + 6.2) = 8.9x + 14.9,
$$[/tex]
which is equivalent to the original expression.
5. Option 5:
[tex]$$
6.2 + 8.7 + 8.9.
$$[/tex]
This option has only constant terms (it does not include an [tex]$x$[/tex] term) and sums to [tex]$6.2 + 8.7 + 8.9 = 23.8$[/tex], so it is not equivalent.
6. Option 6:
[tex]$$
6.2 + 87 + 89x.
$$[/tex]
Here, the [tex]$x$[/tex]-term is [tex]$89x$[/tex] and the constant is [tex]$6.2 + 87 = 93.2$[/tex], which does not match the original expression.
7. Option 7:
[tex]$$
8.9 + 62x + 87.
$$[/tex]
In this option, the variable term is [tex]$62x$[/tex] and the constant is [tex]$8.9 + 87 = 95.9$[/tex]. This also does not match the original expression.
Conclusion: Only Options 3 and 4 simplify to
[tex]$$
8.9x + 14.9,
$$[/tex]
which means they are equivalent to the original expression.
Thus, the expressions equivalent to [tex]$8.9x+6.2+8.7$[/tex] are Options 3 and 4.
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