Final answer:
The law shown by the equality of x 4 and 4 x is the Commutive Law of Multiplication, which states that the order in which two numbers are multiplied does not change the product. This is a fundamental concept in algebra that also applies to addition but not to subtraction and division.
Step-by-step explanation:
The law illustrated by the statement that x 4 is the same as 4 x is known as the Commutive Law of Multiplication. This law states that the order in which two numbers are multiplied does not change the product. For example, if x is 2, then 2 x 4 is 8, and also 4 x 2 is 8, confirming that 2 x 4 equals 4 x 2. The Commutative Law applies to addition as well, where a + b equals b + a. However, it's important to note that this law does not apply to subtraction and division.
When solving equations, one might sometimes multiply or divide both sides of the equation by the same number or expression to maintain the equality, which is a different concept altogether. It is essential to understand these laws and rules as they form the foundation for algebra and are applied in solving equations.