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Answer :
Sure! Let's understand which expressions are equivalent to the expression [tex]\(8.9x + 6.2 + 8.7\)[/tex].
### Step-by-Step Solution
1. Understand the Expression's Form:
- The original expression is [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- We have a term with [tex]\(x\)[/tex] and two constant terms that can be combined.
2. Simplify the Original Expression:
- Combine the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].
- Therefore, the simplified expression is [tex]\(8.9x + 14.9\)[/tex].
3. Check Each Given Expression:
- Now let's compare each of the provided expressions to find which ones are equivalent to [tex]\(8.9x + 14.9\)[/tex].
a) [tex]\(9x + 6 + 9\)[/tex]:
- Simplify to [tex]\(9x + 15\)[/tex], not equal to [tex]\(8.9x + 14.9\)[/tex].
b) [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- Equals [tex]\(8.7x + 15.1\)[/tex], not equal to [tex]\(8.9x + 14.9\)[/tex].
c) [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- Simplifies to [tex]\(8.9x + 14.9\)[/tex], which is equivalent!
d) [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Order of terms doesn't matter in addition, simplifies to [tex]\(8.9x + 14.9\)[/tex], which is equivalent!
e) [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- Simplifies to [tex]\(23.8\)[/tex], no x-term, not equivalent.
f) [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Simplifies to [tex]\(8.9x + 14.9\)[/tex], which is equivalent!
g) [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- Simplifies to [tex]\(14.9 + 6.2x\)[/tex], not equal to [tex]\(8.9x + 14.9\)[/tex].
### Conclusion
The expressions [tex]\(8.9x + 8.7 + 6.2\)[/tex], [tex]\(8.7 + 8.9x + 6.2\)[/tex], and [tex]\(6.2 + 8.7 + 8.9x\)[/tex] are equivalent to the original expression [tex]\(8.9x + 6.2 + 8.7\)[/tex]. Therefore, the correct choices are 3, 4, and 6.
### Step-by-Step Solution
1. Understand the Expression's Form:
- The original expression is [tex]\(8.9x + 6.2 + 8.7\)[/tex].
- We have a term with [tex]\(x\)[/tex] and two constant terms that can be combined.
2. Simplify the Original Expression:
- Combine the constants: [tex]\(6.2 + 8.7 = 14.9\)[/tex].
- Therefore, the simplified expression is [tex]\(8.9x + 14.9\)[/tex].
3. Check Each Given Expression:
- Now let's compare each of the provided expressions to find which ones are equivalent to [tex]\(8.9x + 14.9\)[/tex].
a) [tex]\(9x + 6 + 9\)[/tex]:
- Simplify to [tex]\(9x + 15\)[/tex], not equal to [tex]\(8.9x + 14.9\)[/tex].
b) [tex]\(8.9 + 6.2 + 8.7x\)[/tex]:
- Equals [tex]\(8.7x + 15.1\)[/tex], not equal to [tex]\(8.9x + 14.9\)[/tex].
c) [tex]\(8.9x + 8.7 + 6.2\)[/tex]:
- Simplifies to [tex]\(8.9x + 14.9\)[/tex], which is equivalent!
d) [tex]\(8.7 + 8.9x + 6.2\)[/tex]:
- Order of terms doesn't matter in addition, simplifies to [tex]\(8.9x + 14.9\)[/tex], which is equivalent!
e) [tex]\(6.2 + 8.7 + 8.9\)[/tex]:
- Simplifies to [tex]\(23.8\)[/tex], no x-term, not equivalent.
f) [tex]\(6.2 + 8.7 + 8.9x\)[/tex]:
- Simplifies to [tex]\(8.9x + 14.9\)[/tex], which is equivalent!
g) [tex]\(8.9 + 6.2x + 8.7\)[/tex]:
- Simplifies to [tex]\(14.9 + 6.2x\)[/tex], not equal to [tex]\(8.9x + 14.9\)[/tex].
### Conclusion
The expressions [tex]\(8.9x + 8.7 + 6.2\)[/tex], [tex]\(8.7 + 8.9x + 6.2\)[/tex], and [tex]\(6.2 + 8.7 + 8.9x\)[/tex] are equivalent to the original expression [tex]\(8.9x + 6.2 + 8.7\)[/tex]. Therefore, the correct choices are 3, 4, and 6.
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