Answer :
We start with the original expression:
[tex]$$
8.9x + 6.2 + 8.7.
$$[/tex]
Step 1. Simplify the original expression.
Combine the constant terms:
[tex]$$
6.2 + 8.7 = 14.9.
$$[/tex]
Thus, the expression simplifies to:
[tex]$$
8.9x + 14.9.
$$[/tex]
Step 2. Analyze each option.
1. Option 1:
[tex]$$
9x + 6 + 9.
$$[/tex]
Combine the constants:
[tex]$$
6 + 9 = 15,
$$[/tex]
so the expression becomes:
[tex]$$
9x + 15.
$$[/tex]
The coefficient of [tex]$x$[/tex] is [tex]$9$[/tex] and the constant is [tex]$15$[/tex], which does not match the original expression [tex]$8.9x + 14.9$[/tex].
2. Option 2:
[tex]$$
8.9 + 6.2 + 8.7x.
$$[/tex]
Rearranging, we have the [tex]$x$[/tex]-term and the constants:
[tex]$$
8.7x + \bigl(8.9 + 6.2\bigr) = 8.7x + 15.1.
$$[/tex]
Here the coefficient of [tex]$x$[/tex] is [tex]$8.7$[/tex] and the constant is [tex]$15.1$[/tex], so it is not equivalent to [tex]$8.9x + 14.9$[/tex].
3. Option 3:
[tex]$$
8.9x + 8.7 + 6.2.
$$[/tex]
Combine the constants:
[tex]$$
8.7 + 6.2 = 14.9.
$$[/tex]
This gives:
[tex]$$
8.9x + 14.9.
$$[/tex]
This is exactly the same as the simplified original expression.
4. Option 4:
[tex]$$
8.7 + 8.9x + 6.2.
$$[/tex]
Rearranging the terms (using the commutative property of addition) gives:
[tex]$$
8.9x + (8.7 + 6.2) = 8.9x + 14.9.
$$[/tex]
This matches the original expression exactly.
5. Option 5:
[tex]$$
6.2 + 8.7 + 8.9.
$$[/tex]
Here, there is no [tex]$x$[/tex]-term; adding the numbers:
[tex]$$
6.2 + 8.7 + 8.9 = 23.8,
$$[/tex]
so this is just a constant and is not equivalent to an expression with an [tex]$x$[/tex] term.
6. Option 6:
[tex]$$
6.2 + 8.7 + 8.9x.
$$[/tex]
Rearranging gives:
[tex]$$
8.9x + (6.2 + 8.7) = 8.9x + 14.9.
$$[/tex]
This is equivalent to the original expression.
7. Option 7:
[tex]$$
8.9 + 6.2x + 8.7.
$$[/tex]
Combine the constant terms:
[tex]$$
8.9 + 8.7 = 17.6,
$$[/tex]
yielding:
[tex]$$
6.2x + 17.6.
$$[/tex]
The coefficient of [tex]$x$[/tex] and the constant do not match the original expression.
Step 3. Conclusion
The expressions that are equivalent to the original expression
[tex]$$
8.9x + 14.9
$$[/tex]
are found in Options 3, 4, and 6.
Thus, the correct answers are Options 3, 4, and 6.
[tex]$$
8.9x + 6.2 + 8.7.
$$[/tex]
Step 1. Simplify the original expression.
Combine the constant terms:
[tex]$$
6.2 + 8.7 = 14.9.
$$[/tex]
Thus, the expression simplifies to:
[tex]$$
8.9x + 14.9.
$$[/tex]
Step 2. Analyze each option.
1. Option 1:
[tex]$$
9x + 6 + 9.
$$[/tex]
Combine the constants:
[tex]$$
6 + 9 = 15,
$$[/tex]
so the expression becomes:
[tex]$$
9x + 15.
$$[/tex]
The coefficient of [tex]$x$[/tex] is [tex]$9$[/tex] and the constant is [tex]$15$[/tex], which does not match the original expression [tex]$8.9x + 14.9$[/tex].
2. Option 2:
[tex]$$
8.9 + 6.2 + 8.7x.
$$[/tex]
Rearranging, we have the [tex]$x$[/tex]-term and the constants:
[tex]$$
8.7x + \bigl(8.9 + 6.2\bigr) = 8.7x + 15.1.
$$[/tex]
Here the coefficient of [tex]$x$[/tex] is [tex]$8.7$[/tex] and the constant is [tex]$15.1$[/tex], so it is not equivalent to [tex]$8.9x + 14.9$[/tex].
3. Option 3:
[tex]$$
8.9x + 8.7 + 6.2.
$$[/tex]
Combine the constants:
[tex]$$
8.7 + 6.2 = 14.9.
$$[/tex]
This gives:
[tex]$$
8.9x + 14.9.
$$[/tex]
This is exactly the same as the simplified original expression.
4. Option 4:
[tex]$$
8.7 + 8.9x + 6.2.
$$[/tex]
Rearranging the terms (using the commutative property of addition) gives:
[tex]$$
8.9x + (8.7 + 6.2) = 8.9x + 14.9.
$$[/tex]
This matches the original expression exactly.
5. Option 5:
[tex]$$
6.2 + 8.7 + 8.9.
$$[/tex]
Here, there is no [tex]$x$[/tex]-term; adding the numbers:
[tex]$$
6.2 + 8.7 + 8.9 = 23.8,
$$[/tex]
so this is just a constant and is not equivalent to an expression with an [tex]$x$[/tex] term.
6. Option 6:
[tex]$$
6.2 + 8.7 + 8.9x.
$$[/tex]
Rearranging gives:
[tex]$$
8.9x + (6.2 + 8.7) = 8.9x + 14.9.
$$[/tex]
This is equivalent to the original expression.
7. Option 7:
[tex]$$
8.9 + 6.2x + 8.7.
$$[/tex]
Combine the constant terms:
[tex]$$
8.9 + 8.7 = 17.6,
$$[/tex]
yielding:
[tex]$$
6.2x + 17.6.
$$[/tex]
The coefficient of [tex]$x$[/tex] and the constant do not match the original expression.
Step 3. Conclusion
The expressions that are equivalent to the original expression
[tex]$$
8.9x + 14.9
$$[/tex]
are found in Options 3, 4, and 6.
Thus, the correct answers are Options 3, 4, and 6.
