Axioms to solve Equation:

There are four axioms used for solving these equations:

Axiom 1. If the similar quantity is added to both sides of the equation, the resulting equation is still true.

Axiom 2. If the similar quantity is subtracted from both sides of an equation, the output equation is still true.

Axiom 3. If both sides of an equation are multiplied through the similar quantity, the output equation is still true.

Axiom 4. If both sides of an equation are divided by the similar quantity, except 0, the output equation is still true.

Axiom 1 is known as the addition axiom; Axiom 2 known for the subtraction axiom; Axiom 3 for the multiplication axiom; and Axiom 4 for the division axiom.  These four axioms can be visualized through the balancing of a scale.  Now if the scale is initially balanced, it will remain balanced if the similar weight is added to both sides, if the same weight is erased from both sides, if the weights on both sides are raised through the similar factor, or if the weights on both sides are decreased through the same factor.