Math101 · Independent Ontario learning library
Math101Solving One-Step Equations
A one-step equation isolates its variable with one inverse operation. The goal is not to “move” a term mysteriously but to preserve equality by applying the same legal operation to both sides.
One-step equations establish the balance principle and inverse-operation reasoning used in every later algebraic equation and formula.
Intuition and core definition
A one-step equation isolates its variable with one inverse operation. The goal is not to “move” a term mysteriously but to preserve equality by applying the same legal operation to both sides. Addition and subtraction are inverse operations; multiplication and nonzero division are inverses.
Notation, language, and conditions
Equations may appear as $x+a=b$, $x-a=b$, $ax=b$, or $x/a=b$ with $a\ne0$ where needed. The solution set contains values that satisfy the original. A coefficient includes its sign, so $-3x=12$ requires division by $-3$.
Why this idea matters
A one-step equation is undone with the inverse operation applied equally to both sides, preserving the original equality.
A dependable method
- Identify the operation directly attached to the variable.
- Choose its inverse operation.
- Apply that inverse to both sides and simplify.
- Write the isolated variable and solution clearly.
- Substitute the value into the original equation to verify equality.
