Glossary
Inverse operations
Also written: inverse operation · opposite operations
Definition
Inverse operations undo each other. Addition and subtraction are inverses, and so are multiplication and division. Solving an equation means applying the inverse of whatever was done to the variable.
The four pairs
| Operation | Undone by |
|---|---|
| addition | subtraction |
| subtraction | addition |
| multiplication | division |
| division | multiplication |
Why they solve equations
An equation is a record of what was done to the variable. In , the variable was multiplied by , then was added. Applying the inverses in reverse order retraces that path backwards until the variable stands alone.
The order matters: undo the addition first, then the multiplication. See two-step equations for why reversing a sequence means starting from its end.
Squares and square roots
Squaring and taking a square root are also inverses, with one catch: gives back the size but not the sign. That is where the in completing the square comes from.
Lessons that use this term
- How to Solve One-Step Equations
Solve one-step equations by doing the same inverse operation to both sides, with worked examples, common mistakes, and practice problems with full solutions.
- How to Solve Two-Step Equations
Solve two-step equations by undoing addition first and multiplication second, with worked examples, common mistakes, and practice problems with full solutions.