Always True
Part of the Fundamentals section of Coddy's Math journey. Lesson 47 of 64.
The opposite can happen too. 2(x + 1) = 2x + 2: distribute the left side and both sides read 2x + 2. Subtract 2x from both sides:
2 = 2
A true statement with no x in it. The original equation was true for every value of x (try 0, try 7, try -3): it is an identity, and its solution is "all numbers".
So when the unknown cancels out, the leftover statement decides: false means no solution, true means every number is a solution. Both are complete answers.
Challenge
Solve 3(x - 2) = 3x - 6 and see what the algebra says.
Try it yourself
Solve for x
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