No Solution
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 46 of 64.
Not every equation has a solution. The equation x + 3 = x + 5 says that a number plus 3 equals the same number plus 5. No number can do that. Solve it anyway and see what happens. Subtract x from both sides:
3 = 5
The x terms cancel out, and what is left is a false statement. A false statement means the original equation is false for every value of x. The equation has no solution. Every step was correct. The answer is that no number works.
You cannot tell from the look of an equation whether it has a solution. The equation 2(x + 1) = 2x + 5 looks ordinary. Distribute the left side to get 2x + 2 = 2x + 5. Subtract 2x from both sides and you get 2 = 5. Whenever the x terms cancel out completely, look at the statement that is left. If it is false, the equation has no solution.
Challenge
MediumSolve 2(x + 3) = 2x + 1. Distribute first, then subtract the x terms and look at the statement that is left.
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