The Same to Both Sides
Part of the Fundamentals section of Coddy's Math journey. Lesson 3 of 64.
Picture an equation as a balance scale with the equals sign at the pivot. x + 3 = 8: the left pan holds a box of unknown weight and a 3-kilo weight, the right pan holds 8 kilos, and the scale is level. Take the 3-kilo weight off the left pan and the scale tips, unless you take 3 kilos off the right pan too.
That is the one law of equations: whatever you do to one side, do to the other. Then the two sides stay equal, and the new equation has the same solution as the old one.
Subtract 3 from both sides of x + 3 = 8:
x + 3 - 3 = 8 - 3
On the left, adding 3 and taking 3 away cancel, leaving x by itself. On the right, 8 - 3 is 5:
x = 5
No guessing: the equation itself told you the answer.
Challenge
Solve the equation x + 5 = 12 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