1. **Simplify the expression** $9 - 2x - 7 + 4x$. 2. **Use the Commutative Property** to reorder terms so like terms are together: $$9 + 4x - 7 - 2x$$ 3. **Use the Associative Property** to group like terms: $$ (9 - 7) + (4x - 2x) $$ 4. **Simplify by combining like terms:** $$ 9 - 7 = 2 $$ $$ 4x - 2x = 2x $$ 5. **Final simplified expression:** $$ 2 + 2x $$ --- 6. **Eloise's tiles problem:** - Original expression: $3n + 4 - n + 5$ 7. **Eloise rearranged the tiles using the Commutative Property** (changing order of terms). 8. **Expression representing Eloise's arrangement:** $$ 3n - n + 4 + 5 $$ 9. **Group like terms:** $$ (3n - n) + (4 + 5) $$ 10. **Simplify:** $$ 2n + 9 $$ --- 11. **Simplify the expression $7r - 8r + 13 - 2r + 5$:** 12. **Group like terms:** $$ (7r - 8r - 2r) + (13 + 5) $$ 13. **Simplify the coefficients of $r$:** $$ 7r - 8r = \cancel{7r} - 8r = -1r $$ $$ -1r - 2r = \cancel{-1r} - 2r = -3r $$ 14. **Simplify constants:** $$ 13 + 5 = 18 $$ 15. **Final simplified expression:** $$ -3r + 18 $$