Learner Journey LabsLearner Journey Labs
LMAT 106 · Unit 1 ALEKS · 1.2
Interactive mathematics course

Solve Linear and Quadratic Equations

Build equality and inverse-operation reasoning first, then progress through linear equations, factoring, square roots, completing the square, the quadratic formula, method choice, and modeling. Every topic includes visuals, fully explained examples, prediction-first practice, and feedback.

How to use this course

Follow the topics in order

Each topic teaches one equation-solving concept from its prerequisites and prepares you for the next. Start with Topic 1 if algebra equations are new to you. Return here at any time to reopen a topic or continue from the last one you visited.

Part 1

Equation foundations

  1. What an Equation and Solution MeanInterpret equality and test whether a value is a solution. Open topic
  2. Inverse Operations and CheckingPreserve equality while undoing operations and checking solutions. Open topic
  3. One-Step Addition and Subtraction EquationsIsolate a variable by undoing an added signed number. Open topic
  4. One-Step Multiplication and Division EquationsTurn a nonzero coefficient into 1 using inverse operations. Open topic
Part 2

Solving linear equations

  1. Distributive and Multi-Step Linear EquationsDistribute to every term, simplify, and isolate the variable. Open topic
  2. Combining Like Terms in Linear EquationsCombine only terms with the same variable part before solving. Open topic
  3. Linear Equations with Variables on Both SidesCollect variable terms on one side and constants on the other. Open topic
  4. Linear Equations with Fractions and DecimalsClear denominators or use exact decimal operations deliberately. Open topic
  5. Identity and No-Solution Linear EquationsInterpret a final truth or contradiction as a solution-set result. Open topic
  6. Modeling with Linear EquationsTranslate a rate-and-starting-value situation into an equation. Open topic
Part 3

Factoring and zero products

  1. Recognizing Quadratic Equations and Standard FormIdentify quadratic structure and rewrite it as ax² + bx + c = 0. Open topic
  2. The Zero-Product PropertyTurn a product equal to zero into separate factor equations. Open topic
  3. Factoring Out the Greatest Common FactorExpose simpler factors by removing the shared factor first. Open topic
  4. Factoring Quadratics with Leading Coefficient 1Use a signed sum-product pair to build binomial factors. Open topic
  5. Factoring Quadratics with a Leading Coefficient Other Than 1Verify leading factors, constant factors, and cross-products. Open topic
Part 4

General quadratic methods

  1. Solving Quadratics by Square RootsUse both positive and negative square-root branches. Open topic
  2. Completing the SquareCreate a perfect-square trinomial while preserving equality. Open topic
  3. Using the Quadratic FormulaSubstitute signed coefficients and simplify both formula branches. Open topic
  4. The Discriminant and the Number of Real SolutionsPredict two, one, or no real solutions from b² − 4ac. Open topic
  5. Choosing a Quadratic Solving MethodUse visible equation structure to choose an efficient valid method. Open topic
Part 5

Quadratic modeling

  1. Modeling with Quadratic EquationsBuild a quadratic model and interpret roots within the situation's domain. Open topic