Which concept is closely related to the invention of the equals sign?

The concept of balance in equations is closely related to the invention of the equals sign because the equals sign was introduced as a way to indicate that two expressions hold the same value. In algebra, the principle of maintaining balance is fundamental; both sides of an equation must represent the same quantity for the equation to be valid.

When Robert Recorde first introduced the equals sign in 1557, it served to signify that the expressions on either side of the symbol were equal, emphasizing the importance of equivalence in mathematical expressions. This reflects the idea of balance, as each side of the equation must remain equal to each other through various operations or transformations, illustrating the core principle of algebraic equations.

In contrast, while addition, subtraction, and multiplication are all operations that can be performed on equations, they do not inherently encompass the foundational concept of balance that the equals sign signifies. The equals sign itself is a critical part of establishing and maintaining the equality between two mathematical expressions, making balance in equations the most relevant concept.