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Math
Elementary Algebra

Elementary Algebra

This is the next rung after Prealgebra: a first full course in algebra. It starts by consolidating the arithmetic foundations — real numbers and their properties — and builds from there through solving equations, graphing lines, working with polynomials, factoring, rational and radical expressions, and finally quadratic equations.

Prerequisites: Prealgebra, or comfort with integers, fractions, decimals, and the basic language of algebra. This is advisory, not a gate — start here if the foundations already feel familiar.

Chapters

This book is organized into ten chapters, each broken into short sections you can work through in order.

  • Foundations — whole numbers, the language of algebra, integers, fractions, decimals, the real numbers, their properties, and systems of measurement.
  • Solving Linear Equations and Inequalities — the properties of equality, general strategies for solving, formulas, and linear inequalities.
  • Math Models — problem-solving strategies and applications: percents, mixtures, geometry, uniform motion, and inequalities.
  • Graphs — the rectangular coordinate system, graphing linear equations, intercepts, slope, slope-intercept form, and equations of lines.
  • Systems of Linear Equations — solving by graphing, substitution, and elimination, plus applications and systems of inequalities.
  • Polynomials — adding, subtracting, and multiplying polynomials, exponent properties, dividing, and scientific notation.
  • Factoring — greatest common factor, factoring trinomials and special products, a general strategy, and quadratic equations by factoring.
  • Rational Expressions and Equations — simplifying, operating on, and solving rational expressions, proportions, and variation.
  • Roots and Radicals — square roots, operations on radicals, solving radical equations, higher roots, and rational exponents.
  • Quadratic Equations — the square root property, completing the square, the quadratic formula, applications, and graphing.

About this edition

This book is adapted from OpenStax Elementary Algebra 2e, used under the terms of its Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA 4.0) license. Reviewers who vet or adapt this material are credited in the reviewed_by field of each page.

Foundations