About Algebra Basics

What is Algebra Basics?

Algebra Basics is your first real algebra course. In Pre-Algebra you learned to solve simple equations and work with variables. Now you’ll take those skills much further. This section covers the core techniques that form the backbone of all algebra: multi-step equations, graphing lines, systems of equations, functions, and factoring.

If Pre-Algebra taught you the alphabet, Algebra Basics is where you start writing sentences. You’ll learn to describe relationships between quantities, graph them, and solve problems that involve multiple unknowns at once.

A Brief History

Algebra has roots going back nearly 4,000 years. The Babylonians were solving what we’d now call quadratic equations around 2000 BCE, using verbal instructions carved into clay tablets. The Egyptians had their own methods for working with unknowns, documented in the Rhind Papyrus around 1650 BCE.

But the person who really pulled it all together was al-Khwarizmi, working in Baghdad around 820 CE. His book Al-Jabr (from which we get the word “algebra”) laid out systematic methods for solving equations by “completing” and “balancing” both sides. This was revolutionary. Before al-Khwarizmi, solving equations was more of an art. After him, it was a method anyone could learn.

The notation we use today - letters like x and y, the equals sign, the way we write equations on a line - came much later, mostly from European mathematicians in the 1500s and 1600s. René Descartes gave us the convention of using letters near the end of the alphabet (x, y, z) for unknowns and letters near the beginning (a, b, c) for known quantities. François Viète pioneered using letters for both. Robert Recorde invented the equals sign in 1557 because he was tired of writing “is equal to” over and over. (Relatable.)

The point is that algebra wasn’t handed down from on high. It was built piece by piece by people who needed better tools for solving problems. And the tools they built are exactly what you’re about to learn.

Why We’re Learning It

Algebra is the language that the rest of mathematics is written in. When a physicist writes F = ma, that’s algebra. When an economist models supply and demand, that’s algebra. When a programmer writes a loop that runs until a condition is met, the logic underneath is algebraic.

But you don’t need to be a scientist or programmer to benefit from it. Algebra teaches you to think in terms of relationships. Instead of asking “what’s 15% of 80?” you learn to ask “if something grows by 15% each year, when does it double?” That shift from specific calculations to general reasoning is what makes algebra so powerful.

It’s also the gatekeeper for a lot of practical things. Understanding a mortgage, comparing insurance plans, reading a data report at work, figuring out whether a business idea is financially viable. All of these require algebraic thinking, even if nobody calls it that.

Why It Matters in Real Life

Algebraic thinking shows up constantly:

Comparing job offers (salary vs. hourly, with different benefits)
Understanding loan payments and interest rates
Planning a budget that accounts for variable expenses
Analyzing whether a side project or business idea makes financial sense
Reading graphs and charts and understanding what they actually mean
Solving “when will these two things be equal?” problems (break-even, meeting points, crossover costs)

The common thread is that algebra lets you work with unknowns. And real life is full of unknowns.

What You’ll Learn in This Section

The lessons build on each other in a logical sequence:

Solving multi-step linear equations (distribution, combining terms, variables on both sides)
Literal equations and formulas (solving for one variable in terms of others)
Linear inequalities
Introduction to functions and function notation
Linear functions and slope
Slope-intercept form, point-slope form, and standard form
Graphing linear equations using multiple methods
Systems of equations: graphing, substitution, and elimination
Real-world applications of systems
Introduction to polynomials
Factoring basics: GCF, trinomials, and recognizing patterns

Each lesson includes worked examples, real-world connections, and a quiz.

How to Get the Most Out of This Section

Algebra rewards practice more than almost any other subject. Reading the examples is good. Working them out on paper is better. Trying similar problems on your own is best. If you get stuck, go back one lesson and make sure the foundation is solid before moving forward.

If Pre-Algebra felt comfortable, you’re ready for this. If anything feels shaky, the Pre-Algebra section is right there. No shame in reviewing.