Negative Coefficients
Part of the Fundamentals section of Coddy's Math journey. Lesson 14 of 64.
In -3x = 12 the coefficient is -3: the unknown was multiplied by negative three. Undo it the same way as any coefficient, by dividing both sides by -3, sign included:
-3x/(-3) = 12/(-3)
x = -4
On the left the coefficient divides away to 1. On the right, 12 divided by a negative is negative: -4. Check: -3 × (-4) = 12.
The common mistake is to divide by 3 and forget the sign, landing on x = -4 with the wrong reasoning or on x = 4 with the wrong answer. Divide by the whole coefficient, and the signs take care of themselves.
Challenge
Solve the equation -4x = 24 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