Inverse Operations
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 10 of 64.
There are four operations, and they form two inverse pairs. Addition and subtraction undo each other. Multiplication and division undo each other. To solve a one-step equation, find the operation done to the unknown and apply its inverse to both sides:
If a number was added, subtract it. For x + 7 = 12, subtract 7. If a number was subtracted, add it. For x - 4 = 9, add 4. If the unknown was multiplied by a number, divide by it. For 3x = 12, divide by 3. If the unknown was divided by a number, multiply by it. For x/4 = 5, multiply by 4.
Two things are always true. The step is applied to both sides. And the number you use is the number attached to the unknown, not the number on the other side. In 3x = 12 you divide by 3, not by 12.
If you are not sure which operation was used, say the equation in words. "Three times a number is 12" tells you that the operation is multiplication.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Fundamentals
1What an Equation Is
The EquationFinding the UnknownThe Same to Both SidesSolved Means AloneRecap: First Equations4Two-Step Equations
Two Layers to UndoSubtract, Then DivideAdd, Then DivideA Division InsideNegatives in Two StepsRecap: Two-Step Equations2One-Step Equations
Undoing AdditionUndoing SubtractionUndoing MultiplicationUndoing DivisionInverse OperationsRecap: One-Step Equations5Tidying First
Like TermsTerms and Numbers MixedThe Distributive PropertyDistributing a SubtractionTidy, Then SolveRecap: Tidying First