1. Problem statement: The expression to simplify is $5(2 + w) + 6w$. 2. Formula used: Distributive property $a(b + c) = ab + ac$. 3. Important rules: Use the distributive property to expand products. 4. Important rules: Combine like terms by adding their coefficients when the variable parts match. 5. Important rules: Use the commutative property of addition to reorder terms if desired. 6. Step 1 - expand: Apply the distributive property to $5(2 + w)$ to get $10 + 5w$, so the expression becomes $10 + 5w + 6w$. 7. Reason for Step 1: Distributive property. 8. Step 2 - combine like terms: Add the like terms $5w$ and $6w$ to obtain $11w$, producing $10 + 11w$. 9. Reason for Step 2: Combine like terms (addition of like terms). 10. Step 3 - reorder: Use the commutative property of addition to write $11w + 10$ from $10 + 11w$. 11. Reason for Step 3: Commutative property of addition. 12. Final answer: $11w + 10$.