Gathering the x's
Part of the Fundamentals section of Coddy's Math journey. Lesson 30 of 64.
4x + 3 = x + 15: x-terms on both sides and a number on both sides. Gather the x's first (subtract x from both sides), then the numbers (subtract 3), then divide.
3x + 3 = 15
3x = 12
x = 4
Check: 4 × 4 + 3 = 19 and 4 + 15 = 19.
Which side should the x's live on? Either works. Moving them to the side that already has the larger coefficient keeps the coefficient positive, which is one less sign to think about: here 4x beats x, so the x's go left. It is a convenience, not a rule.
Challenge
Solve the equation 5x + 2 = 2x + 14 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 First6Variables on Both Sides
x on Both SidesGathering the x'sNumbers and x's EverywhereParentheses on One SideWhen x Is NegativeRecap: Both Sides