Answer :
To determine which expressions are equivalent to the expression [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to check each option and verify if they produce the same result when simplified or if any rearrangement matches the structure of the original expression. Let's break it down step by step:
1. Original Expression:
- [tex]\(8.9x + 6.2 + 8.7\)[/tex]
Now, let's analyze each given option:
1. Option 1: [tex]\(9x + 6 + 9\)[/tex]
- This expression is not rearranging or simplifying the original terms. It changes the coefficients and constants. Therefore, it's not equivalent.
2. Option 2: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- Here, the terms are rearranged. The constant terms [tex]\(6.2\)[/tex] and [tex]\(8.7\)[/tex] are at the beginning, and [tex]\(8.9x\)[/tex] comes last. This is just a rearrangement of the original expression, assuming no change in the meaning of [tex]\(8.9x\)[/tex], so it's equivalent.
3. Option 3: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- This is a direct rearrangement of the original expression's terms. The order of addition does not affect the result, so this expression is equivalent.
4. Option 4: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- Again, this is simply a rearrangement of the terms. It maintains the original components without altering their values or relationships. Thus, it's equivalent.
5. Option 5: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- This expression sums constants only and omits the term involving [tex]\(x\)[/tex]. Therefore, it cannot be equivalent to the original expression which includes an [tex]\(x\)[/tex] term.
6. Option 6: [tex]\(2 + 87 + 8.9x\)[/tex]
- This expression has different constants and potentially a misplaced decimal point affecting one of the constants. The structure and values significantly differ from the original, so it's not equivalent.
7. Option 7: [tex]\(8.9 + 6.2x + 8.7\)[/tex]
- This expression misplaces the coefficient [tex]\(8.9\)[/tex] as a constant and changes [tex]\(6.2\)[/tex] to be the coefficient of [tex]\(x\)[/tex]. Thus, it alters the original structure and is not equivalent.
Based on our analysis, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- [tex]\(8.7 + 8.9x + 6.2\)[/tex]
So, the correct equivalent expressions are options 2, 3, and 4.
1. Original Expression:
- [tex]\(8.9x + 6.2 + 8.7\)[/tex]
Now, let's analyze each given option:
1. Option 1: [tex]\(9x + 6 + 9\)[/tex]
- This expression is not rearranging or simplifying the original terms. It changes the coefficients and constants. Therefore, it's not equivalent.
2. Option 2: [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- Here, the terms are rearranged. The constant terms [tex]\(6.2\)[/tex] and [tex]\(8.7\)[/tex] are at the beginning, and [tex]\(8.9x\)[/tex] comes last. This is just a rearrangement of the original expression, assuming no change in the meaning of [tex]\(8.9x\)[/tex], so it's equivalent.
3. Option 3: [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- This is a direct rearrangement of the original expression's terms. The order of addition does not affect the result, so this expression is equivalent.
4. Option 4: [tex]\(8.7 + 8.9x + 6.2\)[/tex]
- Again, this is simply a rearrangement of the terms. It maintains the original components without altering their values or relationships. Thus, it's equivalent.
5. Option 5: [tex]\(6.2 + 8.7 + 8.9\)[/tex]
- This expression sums constants only and omits the term involving [tex]\(x\)[/tex]. Therefore, it cannot be equivalent to the original expression which includes an [tex]\(x\)[/tex] term.
6. Option 6: [tex]\(2 + 87 + 8.9x\)[/tex]
- This expression has different constants and potentially a misplaced decimal point affecting one of the constants. The structure and values significantly differ from the original, so it's not equivalent.
7. Option 7: [tex]\(8.9 + 6.2x + 8.7\)[/tex]
- This expression misplaces the coefficient [tex]\(8.9\)[/tex] as a constant and changes [tex]\(6.2\)[/tex] to be the coefficient of [tex]\(x\)[/tex]. Thus, it alters the original structure and is not equivalent.
Based on our analysis, the expressions that are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex] are:
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex]
- [tex]\(8.9x + 8.7 + 6.2\)[/tex]
- [tex]\(8.7 + 8.9x + 6.2\)[/tex]
So, the correct equivalent expressions are options 2, 3, and 4.
