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 does not change the product. In the equation, \( 5x \) and \( x \cdot 5 \) are equivalent expressions due to the commutative property of multiplication (i.e., \( a \cdot b = b \cdot a \)). By substituting 1 for \( x \), you're testing whether both sides of the equation yield the same result, thus verifying the equality holds true due to this property.
If you substitute \( x = 1 \):
Left side: \( 5(1) + 3 = 5 + 3 = 8 \)
Right side: \( (1) \cdot 5 + 3 = 5 + 3 = 8 \)
Since both sides are equal, it supports the equality in the equation as well as the property.