When my answer is 4=x and I rewrite it as x=4, is that illustrating a property? Why am I able to do that?

My name is Billy

vs
Billy is my name

If I recall, it is called the transitive property

I think that's the symmetric property.

Transitive is
A=B and B=C ==> A=C

When you rewrite the equation 4 = x as x = 4, it is called reversing the order. This is not a specific property but rather a convention we follow in mathematics.

In algebra, equations express relationships between different values and variables. Generally, the equal sign (=) indicates that the expressions on both sides are equivalent. So, when you have 4 = x, it means that the value of x is 4.

However, in certain situations, it may be more convenient to have the variable (in this case x) on the left side of the equation. So, by convention, we rewrite the equation as x = 4, simply reversing the order of the expression.

Both 4 = x and x = 4 convey the same meaning and are mathematically equivalent statements. This reversal does not change the value or meaning of the equation itself, but it can make it easier to work with, especially when solving for the variable or performing further computations.