1. **State the problem:** We are given the expression $5(7 + 2x)$ and its transformations in subsequent lines. We need to identify the property that justifies each step. 2. **Step 1 to Step 2:** From $5(7 + 2x)$ to $35 + 10x$ - This step uses the **Distributive Property** which states that $a(b + c) = ab + ac$. - Here, $5$ is multiplied by both $7$ and $2x$ separately: $5 \times 7 = 35$ and $5 \times 2x = 10x$. 3. **Step 2 to Step 3:** From $35 + 10x$ to $10x + 35$ - This step uses the **Commutative Property of Addition** which states that $a + b = b + a$. - The terms are simply reordered without changing their values. **Final answer:** - Line 1 to Line 2: Distributive Property - Line 2 to Line 3: Commutative Property of Addition