The Distributive Property
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 25 of 64.
You can solve 2(x + 3) = 14 in two ways. The first way is to distribute the 2 over the bracket. That gives 2x + 6 = 14, a two-step equation. Subtract 6 from both sides, then divide by 2:
2x + 6 = 14
2x = 8
x = 4
The second way is to divide both sides by 2 first. That gives x + 3 = 7, and subtracting 3 gives x = 4. Dividing first means you never have to expand the bracket. Both ways give the same solution, because dividing both sides by 2 is allowed and 2 is not zero.
The rule behind the first way is the distributive property: a(b + c) = ab + ac. You will use this rule in many later lessons.
Challenge
MediumSolve the equation 3(x + 5) = 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