x on Both Sides
Part of the Fundamentals section of Coddy's Math journey. Lesson 29 of 64.
5x = 2x + 9 has the unknown on both sides. The plan is to gather all the x's on one side, and the one law does it: subtract 2x from both sides, exactly as you would subtract a number.
5x - 2x = 2x + 9 - 2x
3x = 9
x = 3
Check: 5 × 3 = 15 and 2 × 3 + 9 = 15. Both sides agree.
An x-term is a legitimate thing to add or subtract from both sides; the balance does not care whether the weight is a number or a box. Any equation with x on both sides starts this way.
Challenge
Solve the equation 7x = 3x + 20 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