Math101 · Independent Ontario learning library
Math101Solving Two-Step Equations
A two-step equation requires undoing two operations to isolate the variable. Work in reverse order of how the expression was built while performing the same transformation on both sides.
Two-step equations model fixed fees plus rates, temperature conversions, and simple geometric constraints. The reverse-process idea generalizes beyond memorized “moving terms.”
Intuition and core definition
A two-step equation requires undoing two operations to isolate the variable. Work in reverse order of how the expression was built while performing the same transformation on both sides. For $ax+b=c$, undo the additive $b$ first, then the nonzero multiplicative coefficient $a$.
Notation, language, and conditions
The standard pattern $ax+b=c$ assumes $a\ne0$ for a unique solution. Equivalent equations have the same solution set. Fractional coefficients are valid; the inverse of multiplying by $a$ is dividing by $a$, or multiplying by $1/a$.
Why this idea matters
Two-step equations reverse an affine process in the opposite order from which it was built, while balance is maintained at every line.
A dependable method
- Simplify either side if necessary and identify the variable term.
- Undo addition or subtraction outside the variable term on both sides.
- Undo multiplication or division by the coefficient on both sides.
- Simplify the isolated value without rounding unnecessarily.
- Substitute into the original equation and compare both sides.
