Answer :
To determine which expressions are equivalent to [tex]\(8.9x + 6.2 + 8.7\)[/tex], we need to identify those that can be rearranged or evaluated to yield the same outcome.
Let's break it down step by step:
1. Original expression: The given expression is [tex]\(8.9x + 6.2 + 8.7\)[/tex]. First, we'll simplify this to better identify equivalent expressions.
2. Simplifying the original expression:
[tex]\[
8.9x + 6.2 + 8.7 = 8.9x + (6.2 + 8.7) = 8.9x + 14.9
\][/tex]
3. Examine the provided expressions:
- [tex]\(9x + 6 + 9\)[/tex] simplifies to [tex]\(9x + 15\)[/tex]. This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex] simplifies to [tex]\(8.7x + (8.9 + 6.2) = 8.7x + 15.1\)[/tex]. This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.9x + 8.7 + 6.2\)[/tex] simplifies to [tex]\(8.9x + (8.7 + 6.2) = 8.9x + 14.9\)[/tex]. This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.7 + 8.9x + 6.2\)[/tex] simplifies to [tex]\(8.9x + (8.7 + 6.2) = 8.9x + 14.9\)[/tex]. This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(6.2 + 8.7 + 8.9\)[/tex] or any expression where [tex]\(x\)[/tex] is not multiplied by 8.9 misses the term [tex]\(8.9x\)[/tex]. This is not equivalent.
- [tex]\(6.2 + 8.7 + 8.9x\)[/tex] simplifies to [tex]\(8.9x + (6.2 + 8.7) = 8.9x + 14.9\)[/tex]. This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.9 + 6.2x + 8.7\)[/tex] puts the variable [tex]\(x\)[/tex] on the wrong coefficient; this does not match [tex]\(8.9x + 14.9\)[/tex].
4. Final Equivalent Expressions:
- [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 expressions are equivalent to the original expression [tex]\(8.9x + 6.2 + 8.7\)[/tex]. Any expression that rearranges this correctly without altering coefficients will be equivalent.
Let's break it down step by step:
1. Original expression: The given expression is [tex]\(8.9x + 6.2 + 8.7\)[/tex]. First, we'll simplify this to better identify equivalent expressions.
2. Simplifying the original expression:
[tex]\[
8.9x + 6.2 + 8.7 = 8.9x + (6.2 + 8.7) = 8.9x + 14.9
\][/tex]
3. Examine the provided expressions:
- [tex]\(9x + 6 + 9\)[/tex] simplifies to [tex]\(9x + 15\)[/tex]. This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.9 + 6.2 + 8.7x\)[/tex] simplifies to [tex]\(8.7x + (8.9 + 6.2) = 8.7x + 15.1\)[/tex]. This is not equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.9x + 8.7 + 6.2\)[/tex] simplifies to [tex]\(8.9x + (8.7 + 6.2) = 8.9x + 14.9\)[/tex]. This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.7 + 8.9x + 6.2\)[/tex] simplifies to [tex]\(8.9x + (8.7 + 6.2) = 8.9x + 14.9\)[/tex]. This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(6.2 + 8.7 + 8.9\)[/tex] or any expression where [tex]\(x\)[/tex] is not multiplied by 8.9 misses the term [tex]\(8.9x\)[/tex]. This is not equivalent.
- [tex]\(6.2 + 8.7 + 8.9x\)[/tex] simplifies to [tex]\(8.9x + (6.2 + 8.7) = 8.9x + 14.9\)[/tex]. This is equivalent to [tex]\(8.9x + 14.9\)[/tex].
- [tex]\(8.9 + 6.2x + 8.7\)[/tex] puts the variable [tex]\(x\)[/tex] on the wrong coefficient; this does not match [tex]\(8.9x + 14.9\)[/tex].
4. Final Equivalent Expressions:
- [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 expressions are equivalent to the original expression [tex]\(8.9x + 6.2 + 8.7\)[/tex]. Any expression that rearranges this correctly without altering coefficients will be equivalent.
