Algebra I

Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
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Introduction to algebra

This topic is an overview of the fundamental ideas and tools of algebra.

One-variable linear equations

Learn how to solve linear equations that contain a single variable. For example, solve 2(x+3)=(4x-1)/2+7.

One-variable linear inequalities

Learn how to solve linear inequalities with a single variable. For example, solve -3(x+1)>2x-7. Learn how to solve compound inequalities. For example, solve 2x+1>3 AND -x-5<4.

Units of measurement in modeling

Modeling is an amazing world, full of challenges. In this topic, we will start to think about some general modeling concerns, before we dive into modeling situations with different kinds of functions and equations throughout the Algebra curriculum.

Two-variable linear equations

Learn about linear equations that contain two variables, and how these can be represented by graphical lines and tables of values.

Functions

Functions are mathematical entities that assign unique outputs to given inputs. Sounds simple? Think again! In this topic you will evaluate, graph, analyze, and create various types of functions.

Linear equations and functions word problems

Solve various word problems that involve real world relationships that can be represented by linear equations or functions.

Sequences

Learn about the various ways in which we can define sequences; Use and construct arithmetic and geometric sequences.

Systems of linear equations

Learn how to interpret solutions to systems of linear equations and solve them.

Two-variable linear inequalities

In this topic, we study inequalities like x+2y>5 and graph them. This helps us see their solutions. We also explore systems of inequalities (multiple inequalities at the same time) and use them to describe real-world situations.

Absolute value equations, functions, and inequalities

Learn how to solve absolute value equations, how to graph absolute value functions, and how to solve absolute value inequalities.

Expressions with rational exponents and radicals

Learn about expressions with rational exponents like x^(2/3), about radical expressions like √(2t^5), and about the relationship between these two forms of representation. Learn how to evaluate and simplify such expression.

Introduction to exponential functions

Learn how to construct, analyze, graph, and interpret basic exponential functions of the form f(x)=a*r^x.

Introduction to polynomials

Learn how to add, subtract, and multiply polynomial expressions. For example, write (2x+3)(x-1) as 2x^2+x-3.

Polynomial factorization

Learn how to write polynomial expressions as the product of linear factors. For example, write x^2+3x+2 as (x+1)(x+2).

Quadratic equations and functions

Learn how to solve quadratic equations, and how to analyze and graph quadratic functions.

Rational and irrational numbers

Learn about irrational numbers and how to identify them.

Seeing structure in expressions

Learn how to use algebra in order to solve problems that involve variables whose values are unknown.

Miscellaneous

Introduction to algebra

This topic is an overview of the fundamental ideas and tools of algebra.
Community Questions
All content in “Introduction to algebra”

Overview and history of algebra

Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway? This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.

Introduction to variables

Wait, why are we using letters in math? How can an 'x' represent a number? What number is it? This tutorial is great if you're just beginning to delve into the world of variables and expressions.

Interpreting linear expressions

Any expression (mathematical or otherwise) has meaning. Help us match the linear expression to the meaning options given. In some cases, more than one meaning may apply.