1. The problem is to simplify the expression $5(2 + w) + 6w$ step-by-step and identify the reason for each step. 2. Start with the given expression: $$5(2 + w) + 6w$$ This is the original expression provided. 3. Apply the distributive property, which states $a(b + c) = ab + ac$: $$5 \times 2 + 5 \times w + 6w = 10 + 5w + 6w$$ This step distributes the 5 across the terms inside the parentheses. 4. Combine like terms. The terms $5w$ and $6w$ are like terms because they both contain $w$: $$10 + (5w + 6w) = 10 + 11w$$ Adding the coefficients $5 + 6 = 11$. 5. Rearrange the terms to write the expression in standard form (variable term first): $$11w + 10$$ This is justified by the commutative property of addition, which allows changing the order of terms. Final simplified expression is: $$11w + 10$$