The concept states that if the same quantity is added to both sides of an equation, the equality remains valid. Symbolically, if a = b, then a + c = b + c. For example, given the equation x – 3 = 7, adding 3 to both sides (x – 3 + 3 = 7 + 3) results in x = 10, preserving the equivalence.
This principle is fundamental to algebraic manipulation and equation solving. Its application allows for isolating variables and simplifying equations without altering the solution set. The concepts historical roots are intertwined with the development of algebra as a formal system, providing a reliable method for maintaining balance in mathematical expressions.