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Answer :
To determine which expressions are equivalent to [tex]\( 8.9x + 6.2 + 8.7 \)[/tex], we need to focus on rearranging the terms without changing their values, because equivalent expressions can have the terms in any order.
Let's examine each option to see if it matches the original expression by just rearranging terms:
1. [tex]\( 9x + 6 + 9 \)[/tex]:
- This expression has different coefficients and constants than the original. It's not equivalent.
2. [tex]\( 8.9 + 6.2 + 8.7x \)[/tex]:
- Here, the terms are not grouped correctly. The coefficient [tex]\( 8.9 \)[/tex] should be with [tex]\( x \)[/tex], making it not equivalent.
3. [tex]\( 8.9x + 8.7 + 6.2 \)[/tex]:
- This expression simply rearranges the terms of the original expression. It's equivalent.
4. [tex]\( 8.7 + 8.9x + 6.2 \)[/tex]:
- Like the previous, this is a rearrangement of terms. It's equivalent.
5. [tex]\( 6.2 + 8.7 + 8.9 \)[/tex]:
- This expression is missing the [tex]\( x \)[/tex] term, making it not equivalent.
6. [tex]\( 6.2 + 8.7 + 8.9x \)[/tex]:
- This is another correct rearrangement of terms. It's equivalent.
7. [tex]\( 8.9 + 6.2x + 8.7 \)[/tex]:
- The term [tex]\( 6.2x \)[/tex] is incorrect since it alters the structure of the original expression. Not equivalent.
The expressions that are equivalent 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]
These options have the same terms, just rearranged, making them equivalent.
Let's examine each option to see if it matches the original expression by just rearranging terms:
1. [tex]\( 9x + 6 + 9 \)[/tex]:
- This expression has different coefficients and constants than the original. It's not equivalent.
2. [tex]\( 8.9 + 6.2 + 8.7x \)[/tex]:
- Here, the terms are not grouped correctly. The coefficient [tex]\( 8.9 \)[/tex] should be with [tex]\( x \)[/tex], making it not equivalent.
3. [tex]\( 8.9x + 8.7 + 6.2 \)[/tex]:
- This expression simply rearranges the terms of the original expression. It's equivalent.
4. [tex]\( 8.7 + 8.9x + 6.2 \)[/tex]:
- Like the previous, this is a rearrangement of terms. It's equivalent.
5. [tex]\( 6.2 + 8.7 + 8.9 \)[/tex]:
- This expression is missing the [tex]\( x \)[/tex] term, making it not equivalent.
6. [tex]\( 6.2 + 8.7 + 8.9x \)[/tex]:
- This is another correct rearrangement of terms. It's equivalent.
7. [tex]\( 8.9 + 6.2x + 8.7 \)[/tex]:
- The term [tex]\( 6.2x \)[/tex] is incorrect since it alters the structure of the original expression. Not equivalent.
The expressions that are equivalent 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]
These options have the same terms, just rearranged, making them equivalent.
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