To identify the properties that justify the steps between the lines, let's analyze each line:
Line 1 to Line 2:
- Line 1: \(10(3 + 2x)\)
- Line 2: \(10(2x + 3)\)
The transition from Line 1 to Line 2 involves rearranging the terms inside the parentheses. This is justified by the Commutative Property of Addition, which states that \(a + b = b + a\).
Line 2 to Line 3:
- Line 2: \(10(2x + 3)\)
- Line 3: \(20x + 30\)
The transition from Line 2 to Line 3 involves distributing \(10\) across the terms inside the parentheses. This is justified by the Distributive Property, which states that \(a(b + c) = ab + ac\).
In summary:
- Line 1 to Line 2: Commutative Property of Addition
- Line 2 to Line 3: Distributive Property