Substituting 1 for \( x \) in the equation \( 5x + 3 = x \cdot 5 + 3 \) is a test case for the Commutative Property of multiplication.
This property states that changing the order of the factors in a multiplication operation does not change the product. In this equation, \( 5x \) and \( x \cdot 5 \) represent the same product, thus demonstrating the commutative nature of multiplication.
If you evaluate both sides by substituting \( 1 \) for \( x \):
For the left-hand side: \[ 5(1) + 3 = 5 + 3 = 8 \]
For the right-hand side: \[ 1 \cdot 5 + 3 = 5 + 3 = 8 \]
Both sides equal \( 8 \), confirming the equality holds true, which tests the overall validity of the equality rather than a specific property application for this substitution. However, the crucial multiplication relationship exhibits the Commutative Property in action.
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