Two Layers to Undo
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 17 of 64.
A two-step equation does two things to the unknown. In 2x + 3 = 11, x is first multiplied by 2, and then 3 is added. To get x alone, undo the two operations in reverse order. The last operation done is the first one undone. So subtract 3 first, and divide by 2 second:
2x + 3 - 3 = 11 - 3
2x = 8
2x/2 = 8/2
x = 4
Subtracting 3 removed the added number, and dividing by 2 removed the coefficient.
In 2x + 3 = 11, x is multiplied by 2 and then 3 is added. Undo those operations in reverse order: subtract 3, then divide by 2. Dividing by 2 first also works, but it gives x + 3/2 = 11/2, with fractions.
Challenge
EasySolve 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