Negative Coefficients
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 14 of 64.
In -3x = 12, the coefficient of x is -3. The unknown was multiplied by negative three. Undo it the same way as any coefficient. Divide both sides by -3, with its sign:
-3x/(-3) = 12/(-3)
x = -4
On the left, -3 divided by -3 is 1, so x is alone. On the right, 12 divided by a negative number is negative, so the answer is -4. Check: -3 × (-4) = 12.
In -3x = 12, dividing both sides by -3 gives x = -4 in one step. If you divide by 3 instead, you get -x = 4, and you still need to multiply both sides by -1.
Challenge
EasySolve 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