Answer :
To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to simplify each option and compare it to the original expression.
Here's how you can evaluate each expression:
1. Original Expression: [tex]\(8.9x + 6.2 + 8.7\)[/tex]
Simplify the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].
So, the original expression simplifies to [tex]\(8.9x + 14.9\)[/tex].
Now, let's check each of the given options:
1. Option 1: [tex]\(9x + 6 + 9\)[/tex]
Simplify the constants: [tex]\(6 + 9 = 15\)[/tex].
So, this becomes [tex]\(9x + 15\)[/tex].
Compare: [tex]\(9x + 15\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
2. Option 2: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
Simplify the constants: [tex]\(8.9 + 6.2 = 15.1\)[/tex].
So, this becomes [tex]\(15.1 + 8.7x\)[/tex].
Compare: [tex]\(15.1 + 8.7x\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
3. Option 3: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex].
So, this matches [tex]\(8.9x + 14.9\)[/tex].
Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].
4. Option 4: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex].
So, this becomes [tex]\(8.9x + 14.9\)[/tex].
Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].
5. Option 5: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
Simplify the entire sum: [tex]\(6.2 + 8.7 + 8.9 = 23.8\)[/tex].
This expression is just a constant: [tex]\(23.8\)[/tex].
Compare: [tex]\(23.8\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
6. Option 6: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
Simplify the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].
So, this becomes [tex]\(14.9 + 8.9x\)[/tex].
Rearrange to match: [tex]\(8.9x + 14.9\)[/tex].
Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].
7. Option 7: [tex]\(8.9 + 6.2x + 8.7\)[/tex]
Simplify the constants: [tex]\(8.9 + 8.7 = 17.6\)[/tex].
So, this becomes [tex]\(17.6 + 6.2x\)[/tex].
Compare: [tex]\(17.6 + 6.2x\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
The equivalent expressions 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]
Here's how you can evaluate each expression:
1. Original Expression: [tex]\(8.9x + 6.2 + 8.7\)[/tex]
Simplify the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].
So, the original expression simplifies to [tex]\(8.9x + 14.9\)[/tex].
Now, let's check each of the given options:
1. Option 1: [tex]\(9x + 6 + 9\)[/tex]
Simplify the constants: [tex]\(6 + 9 = 15\)[/tex].
So, this becomes [tex]\(9x + 15\)[/tex].
Compare: [tex]\(9x + 15\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
2. Option 2: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
Simplify the constants: [tex]\(8.9 + 6.2 = 15.1\)[/tex].
So, this becomes [tex]\(15.1 + 8.7x\)[/tex].
Compare: [tex]\(15.1 + 8.7x\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
3. Option 3: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex].
So, this matches [tex]\(8.9x + 14.9\)[/tex].
Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].
4. Option 4: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
Simplify the constants: [tex]\(8.7 + 6.2 = 14.9\)[/tex].
So, this becomes [tex]\(8.9x + 14.9\)[/tex].
Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].
5. Option 5: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
Simplify the entire sum: [tex]\(6.2 + 8.7 + 8.9 = 23.8\)[/tex].
This expression is just a constant: [tex]\(23.8\)[/tex].
Compare: [tex]\(23.8\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
6. Option 6: [tex]\(6.2 + 8.7 + 8.9x\)[/tex]
Simplify the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].
So, this becomes [tex]\(14.9 + 8.9x\)[/tex].
Rearrange to match: [tex]\(8.9x + 14.9\)[/tex].
Compare: [tex]\(8.9x + 14.9\)[/tex] is equivalent to [tex]\(8.9x + 14.9\)[/tex].
7. Option 7: [tex]\(8.9 + 6.2x + 8.7\)[/tex]
Simplify the constants: [tex]\(8.9 + 8.7 = 17.6\)[/tex].
So, this becomes [tex]\(17.6 + 6.2x\)[/tex].
Compare: [tex]\(17.6 + 6.2x\)[/tex] is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
The equivalent expressions 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]
