The principle that allows the same quantity to be added to both sides of an equation without changing the equation’s validity is a fundamental concept in algebra. For instance, if one has the equation x – 3 = 7, adding 3 to both sides maintains the equality, resulting in x – 3 + 3 = 7 + 3, which simplifies to x = 10. This isolates the variable and solves for its value, demonstrating the property in action.
The significance of this property lies in its ability to manipulate equations while preserving their truth. This permits the simplification and solution of complex algebraic expressions. Historically, understanding this property has been crucial in the development of more advanced mathematical concepts and problem-solving techniques. It provides a cornerstone for manipulating equations in numerous fields, including physics, engineering, and economics.
