Linear Equations Summary

Algebra 1 · Axiom Academy

SUMMARY Linear Equations Summary A review of Unit 2 — solving linear equations and inequalities with the balance method, and graphing their solution sets. Solving an equation means isolating the variable — finding the one value that makes both sides equal. The balance principle drives everything: any operation done to one side must be done to the other. Inverse operations peel away whatever surrounds the variable — addition undoes subtraction, multiplication undoes division, and vice versa. An inequality has a whole range of solutions, solved the same way as an equation, with one twist. The Golden Rule: multiplying or dividing both sides by a negative number flips the inequality sign. Core Concept Solving Equations: The Balance Principle Find the single value for a variable that makes the equation true by isolating it on one side. Picture a balance scale: whatever operation you do to one side, you must do to the other to keep it level. When to use: any equation — undo operations in reverse order with their inverses. Multi-step strategy: first simplify each side (distribute, combine like terms), then isolate. Watch out for: forgetting to apply an operation to both sides breaks the balance. Core Concept Solving Inequalities: Ranges of Solutions An inequality asks for the entire range of values that make it true — the solution is a set of numbers, not a single answer. You use the same balance principle and inverse operations as an equation.

This is the written version of the interactive lesson above. See the full Algebra 1 course.