Let's identify the properties that justify each step in the provided lines:
Line 1 to Line 2: \[(x+10)(5+3x) \rightarrow (x+10)(3x+5)\]
Justification: Commutative Property of Addition
(You rearranged the terms inside the parentheses from \(5 + 3x\) to \(3x + 5\). This is allowed because the order of addition does not affect the sum.)
Line 2 to Line 3: \[(x+10)(3x+5) \rightarrow (3x+5)(x+10)\]
Justification: Commutative Property of Multiplication
(You rearranged the factors from \((x+10)(3x+5)\) to \((3x+5)(x+10)\). This is permitted since the order of multiplication does not affect the product.)
In summary:
- Line 1 to Line 2: Commutative Property of Addition
- Line 2 to Line 3: Commutative Property of Multiplication