Question

Substituting 1 for x in the equation 5x + 3=x⋅5 + 3 is a test case for which property?(1 point)
Responses

The Commutative Property of Multiplication
The Commutative Property of Multiplication

The Commutative Property of Addition
The Commutative Property of Addition

The Associative Property of Multiplication
The Associative Property of Multiplication

The Associative Property of Addition

Answer 1

The equation \(5x + 3 = x \cdot 5 + 3\) can be evaluated for \(x = 1\) to check its validity. When we substitute \(1\) for \(x\), both sides of the equation simplify as follows:

- On the left side: \(5(1) + 3 = 5 + 3 = 8\)
- On the right side: \(1 \cdot 5 + 3 = 5 + 3 = 8\)

Both sides are equal when \(x = 1\), which confirms that they produce the same result.

This equation illustrates the **Commutative Property of Multiplication**, which states that changing the order of multiplication does not change the product (i.e., \(a \cdot b = b \cdot a\)). In this case, \(5\) and \(x\) are being multiplied, and switching their positions (as \(x \cdot 5\) instead of \(5 \cdot x\)) demonstrates this property.

So, the correct response is:

**The Commutative Property of Multiplication**