Equivalent Expressions 162A10

1. **State the problem:** We want to find which expressions are equivalent to $$8.9 x + 6.2 + 8.7$$. 2. **Recall the rules:** Equivalent expressions have the same terms combined in the same way. Addition is commutative, so order of addition does not matter, but coefficients and variables must match. 3. **Analyze each option:** - $9 x + 6 + 9$ differs because $9 x \neq 8.9 x$ and constants differ. - $8.9 + 6.2 + 8.7 x$ has $8.7 x$ instead of $8.9 x$, so not equivalent. - $8.9 x + 8.7 + 6.2$ rearranges constants but keeps $8.9 x$, so equivalent. - $8.7 + 8.9 x + 6.2$ same as above, equivalent. - $6.2 + 8.7 + 8.9$ all constants, no $x$ term, so not equivalent. - $6.2 + 8.7 + 8.9 x$ same terms as original, order changed, equivalent. - $8.9 + 6.2 x + 8.7$ has $6.2 x$ instead of $8.9 x$, so not equivalent. 4. **Final answer:** The equivalent expressions are: $$8.9 x + 8.7 + 6.2$$ $$8.7 + 8.9 x + 6.2$$ $$6.2 + 8.7 + 8.9 x$$