No Solution
Part of the Fundamentals section of Coddy's Math journey. Lesson 46 of 64.
Not every equation has a solution. x + 3 = x + 5 says a number plus 3 equals the same number plus 5, which no number can manage. Solve it anyway and watch what the algebra says: subtract x from both sides.
3 = 5
The unknown vanished and left a false statement. That is the algebra's way of saying the original equation was false for every x: it has no solution. Nothing went wrong in the moves; the answer is that there is no answer.
You will not see it coming from the shape alone. 2(x + 1) = 2x + 5 looks ordinary, distributes to 2x + 2 = 2x + 5, and collapses to 2 = 5. Whenever the x-terms cancel out entirely, look at what is left: a false statement means no solution.
Challenge
Solve 2(x + 3) = 2x + 1 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