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Answer :
Sure, let's solve this step by step.
We start with the given expression:
[tex]\[ 8.9x + 6.2 + 8.7 \][/tex]
We need to identify which of the provided expressions are equivalent to this expression.
Let's analyze each option:
1. [tex]\( 9x + 6 + 9 \)[/tex]
- This is not equivalent because the coefficients and constants are different. The given expression has coefficients 8.9 and constants 6.2 and 8.7, not 9 and 6.
2. [tex]\( 8.9 + 6.2 + 8.7x \)[/tex]
- This is not equivalent because the term 8.9 is not multiplied by [tex]\(x\)[/tex]. The given expression has [tex]\(8.9x\)[/tex].
3. [tex]\( 8.9x + 8.7 + 6.2 \)[/tex]
- This is equivalent. The terms are just rearranged, but the values and their respective operations (addition in this case) are the same.
4. [tex]\( 8.7 + 8.9x + 6.2 \)[/tex]
- This is equivalent. Again, the order of the terms is different, but it includes all the original terms with their correct coefficients and constants.
5. [tex]\( 6.2 + 8.7 + 8.9 \)[/tex]
- This is not equivalent because [tex]\( 8.9 \)[/tex] is a constant here, not multiplied by [tex]\( x \)[/tex].
6. [tex]\( 6.2 + 8.7 + 8.9x \)[/tex]
- This is equivalent. The order is different, but the terms and their coefficients are correct.
7. [tex]\( 8.9 + 6.2x + 8.7 \)[/tex]
- This is not equivalent because [tex]\( 6.2 \)[/tex] is the coefficient of [tex]\( x \)[/tex] here, instead of [tex]\( 8.9 \)[/tex].
The equivalent expressions are therefore:
[tex]\[ 8.9x + 8.7 + 6.2 \][/tex]
[tex]\[ 8.7 + 8.9x + 6.2 \][/tex]
[tex]\[ 6.2 + 8.7 + 8.9x \][/tex]
So, the correct options are:
[tex]\[ \boxed{3, 4, 6} \][/tex]
We start with the given expression:
[tex]\[ 8.9x + 6.2 + 8.7 \][/tex]
We need to identify which of the provided expressions are equivalent to this expression.
Let's analyze each option:
1. [tex]\( 9x + 6 + 9 \)[/tex]
- This is not equivalent because the coefficients and constants are different. The given expression has coefficients 8.9 and constants 6.2 and 8.7, not 9 and 6.
2. [tex]\( 8.9 + 6.2 + 8.7x \)[/tex]
- This is not equivalent because the term 8.9 is not multiplied by [tex]\(x\)[/tex]. The given expression has [tex]\(8.9x\)[/tex].
3. [tex]\( 8.9x + 8.7 + 6.2 \)[/tex]
- This is equivalent. The terms are just rearranged, but the values and their respective operations (addition in this case) are the same.
4. [tex]\( 8.7 + 8.9x + 6.2 \)[/tex]
- This is equivalent. Again, the order of the terms is different, but it includes all the original terms with their correct coefficients and constants.
5. [tex]\( 6.2 + 8.7 + 8.9 \)[/tex]
- This is not equivalent because [tex]\( 8.9 \)[/tex] is a constant here, not multiplied by [tex]\( x \)[/tex].
6. [tex]\( 6.2 + 8.7 + 8.9x \)[/tex]
- This is equivalent. The order is different, but the terms and their coefficients are correct.
7. [tex]\( 8.9 + 6.2x + 8.7 \)[/tex]
- This is not equivalent because [tex]\( 6.2 \)[/tex] is the coefficient of [tex]\( x \)[/tex] here, instead of [tex]\( 8.9 \)[/tex].
The equivalent expressions are therefore:
[tex]\[ 8.9x + 8.7 + 6.2 \][/tex]
[tex]\[ 8.7 + 8.9x + 6.2 \][/tex]
[tex]\[ 6.2 + 8.7 + 8.9x \][/tex]
So, the correct options are:
[tex]\[ \boxed{3, 4, 6} \][/tex]
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