When x Is Negative
Part of the Fundamentals section of Coddy's Math journey. Lesson 33 of 64.
10 - x = 2x + 1: the x on the left has coefficient -1. Gathering toward the larger coefficient means moving it to the right: add x to both sides.
10 = 3x + 1
9 = 3x
3 = x
Swap sides for the usual form, x = 3. Check: 10 - 3 = 7 and 2 × 3 + 1 = 7.
Adding an x-term to both sides is as legal as subtracting one, and it is the natural move whenever an x has a minus sign in front. You could instead subtract 2x from both sides and get 10 - 3x = 1, which is also fine; it just carries a negative coefficient to the end.
Challenge
Solve the equation 20 - 2x = 3x + 5 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