Always True
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 47 of 64.
The opposite can happen too. Take the equation 2(x + 1) = 2x + 2. Distribute the left side, and both sides become 2x + 2. Subtract 2x from both sides:
2 = 2
What is left is a true statement with no x in it. A true statement means the original equation is true for every value of x. Try x = 0, x = 7 or x = -3, and both sides always agree. An equation like this is called an identity, and its solution is all numbers.
When the unknown cancels out, look at the statement that is left. If it is false, the equation has no solution. If it is true, every number is a solution. Both of these are complete answers.
Challenge
MediumSolve 3(x - 2) = 3x - 6. Distribute first, then compare the two sides.
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