The first of the two fundamental tools concerns addition and subtraction: we can “move” a term from one side to the other provided we change its sign.
Property — First principle of equivalence
Adding or subtracting the same quantity to both sides, the equation obtained is equivalent to the original one (that is, it has the same solutions).
In practice, this principle justifies the “transfer” of a term from one side to the other by changing its sign: it is exactly the operation that the ancient algebraists called al-jabr.
Links
Topics: First-degree equations
Concepts: Equation · Principle of equivalence
Methods: First-degree equation
Skills: Solving equations