Two Layers to Undo
Part of the Fundamentals section of Coddy's Math journey. Lesson 17 of 64.
2x + 3 = 11 does two things to the unknown: first it doubles it, then it adds 3. To get x back, undo the layers in reverse order: the last thing done is the first thing undone. So: subtract 3 first, divide by 2 second.
2x + 3 - 3 = 11 - 3
2x = 8
2x/2 = 8/2
x = 4
Think of wrapping a present: paper first, then ribbon. Unwrapping starts with the ribbon. Here the "ribbon" is the +3 sitting outermost, and the "paper" is the coefficient 2 hugging the x. Undoing the coefficient first is legal too, but it drags the 3 into a fraction (x + 3/2 = 11/2), which is more work than it needs to be.
Challenge
Solve the equation 3x + 4 = 19 for x.
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