Like Terms
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 23 of 64.
In 3x + 2x = 15, the unknown appears twice on the same side. Before you undo anything, collect the two terms into one. Three x's and two more x's make five x's, in the same way that three apples and two apples make five apples.
5x = 15
x = 3
After collecting, the equation has only one x-term. Divide both sides by 5 and you get x = 3.
Terms with the same letter to the same power are like terms. To combine like terms, add their coefficients: 3x + 2x = 5x, 7x - 4x = 3x, x + x = 2x. Unlike terms stay apart. 3x + 2 cannot be shortened, because an x-term and a plain number are different kinds of term.
Collect like terms whenever a side has more than one x-term. Solving is easier when each side is as short as it can be.
Challenge
MediumSolve the equation 4x + 3x = 28 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