The Distributive Property
Part of the Fundamentals section of Coddy's Math journey. Lesson 25 of 64.
2(x + 3) = 14 multiplies a whole bracket by 2. Two roads lead out. The first distributes the 2 over both terms inside: 2(x + 3) = 2x + 6, and then it is a two-step equation.
2x + 6 = 14
2x = 8
x = 4
The second road treats the bracket as one thing multiplied by 2 and divides both sides by 2 straight away: x + 3 = 7, so x = 4. That is shorter here because 14 divides evenly by 2. When it does not (2(x + 3) = 15), distributing keeps the fractions away for one more step. Both roads are always legal.
The distributive property itself, a(b + c) = ab + ac, is one of the few rules you will use in every chapter from here on.
Challenge
Solve 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