Linear equations
A number is hidden behind a letter, and the letter is never squared. How do you find the number, and how do you know you have all of them?
Where you are 11 inside
What this area is about
A linear equation in one unknown is one where, once each side is simplified, the unknown appears only to the first power: ax + b = cx + d. Solving it means finding every number that makes the sentence true, by moves that can never change the answer.
How these fit together
The ground rules. What a solution is says what you are looking for and how to check it. Inverse operations and the properties of equality say which moves are allowed (never dividing by 0).
The core procedures, each built on the one before: one-step equations, two-step equations px + q = r with p \ne 0, multi-step equations that need tidying first, and equations with the unknown on both sides.
A result about outcomes. No solution, one solution, or every number explains what it means when the unknown vanishes.
Applications of the core. Equations of the form p(x+q)=r from word problems, equations from proportions and percents, absolute value equations (two linear cases), and literal equations that rearrange formulas.
A path through it
What a solution is, then the properties of equality, one-step and two-step equations. After two-step equations come p(x + q) = r, proportions and multi-step equations. Multi-step equations lead to absolute value equations and to variables on both sides, which open the three outcomes and literal equations.
Next: inequalities, linear relationships and rational equations.