Substituting 1 for \( x \) in the equation \( (x \cdot 3) = 5(x \cdot 3) \) can be understood through the properties of numbers.
- If you substitute \( x = 1 \), the left side becomes \( 1 \cdot 3 = 3 \).
- The right side becomes \( 5(1 \cdot 3) = 5 \cdot 3 = 15 \).
This substitution does not demonstrate any of the properties explicitly because the equation becomes \( 3 \neq 15 \).
However, looking at the form of the equation \( (x \cdot 3) = 5(x \cdot 3) \), it highlights how multiplication affects both sides of an equation, primarily indicating the distinction between a number and a multiple of that number.
This scenario aligns more with examining the distribution rather than any associative or commutative property directly.
Let's summarize the properties given:
A. Associative Property of Multiplication: This property states that when multiplying three or more numbers, the way in which they are grouped does not change the product.
B. Associative Property of Addition: This property states that the way in which numbers are grouped does not change their sum.
C. Commutative Property of Multiplication: This property states that changing the order of the factors does not change the product.
D. Commutative Property of Addition: This property states that changing the order of the numbers does not change the sum.
Since neither associative nor commutative properties are demonstrated directly through substitution in this case, the action of substitution in the original expression does not distinctly highlight any one of these properties.
However, in a more abstract sense, utilizing a specific value to explore an equation can give insight into the integrity of these properties, particularly the Commutative Property of Multiplication as it deals with maintaining equality during multiplication.
So, the most fitting choice would be:
C. The Commutative Property of Multiplication.