Question

State the basic axiom of algebra that is represented. $$2 x+3=3+2 x$$

Short answer

The basic axiom of algebra represented by the equation \(2x +3 = 3 + 2x\) is the Commutative Property of Addition.

Step-by-step solution

Identify the Transferable Components

Firstly, observe the given equation \(2x +3 = 3 + 2x\). It can be noticed that these are two expressions that are considered equal, despite the order of their components being different.

Recognize the Axiom

At a glance of both sides of the equation, we can identify that not only the numbers are moved around but also the entire terms. This swapping of terms without altering the equality corresponds to the commutative property of addition. This particular property allows for the order of terms to be changed without affecting the result.