What is preservation of equality in math?

Preservation of equality in mathematics refers to the principle that if two quantities are equal, any operation performed on one side of the equation must also be performed on the other side to maintain that equality. For example, if ( a = b ), then adding the same value ( c ) to both sides results in ( a + c = b + c ). This principle ensures that equations remain balanced and valid during manipulation. It is fundamental to solving equations and maintaining logical consistency in mathematical reasoning.