Substituting 1 for x in the equation 5x + 3 = x times 5 +3 is a test case for which property?

The Associative Property of Addition
The Associative Property of Multiplication
The Communitive Property of Addition
The Communitve Property of Multiplication

1 answer

Substituting 1 for \( x \) in the equation \( 5x + 3 = x \times 5 + 3 \) is a test case for the Commutative Property of Addition.

This is because the expression on both sides can be interpreted in terms of the basic operations performed, and specifically, the rearrangement of terms can be demonstrated.

In this context, when substituting 1 for \( x \), both sides evaluate to the same value, showcasing the commutative nature of addition:

  • Left side: \( 5(1) + 3 = 5 + 3 = 8 \)
  • Right side: \( 1 \times 5 + 3 = 5 + 3 = 8 \)

Thus, the equality holds, supported by the commutative property which states that changing the order of addition does not change the sum.