For middle school and high school students, algebra can be one of the most difficult maths topics. It covers basic operations such as addition, subtraction, multiplication and division. Another important part of algebra is number theory. This includes natural numbers, integers, fractions and so on. Finally, the part that many students seem to need most help with is solving equations for x (or any variable). To guide you with studying algebra, we put together this algebra study guide. This is an overview of topics and references for further help.

Algebra Topics

Algebra roughly covers the areas of basic operations, number theory and solving an equation for a variable. You should study these algebra topics in this order.

Basic Operations

You should understand what an operator is and know about basic operations. These are addition, subtraction, multiplication and division. Apart from just knowing how to add or divide two numbers, you should also know about commutativity and associativity. Finally, to solve equations containing multiple operations, you need to know the order of operations and calculating with brackets. For more difficult problems, you will also need to know about operations like exponentiation, square roots etc.

Number Theory

The basic operations can be used with different kinds of numbers. Those different kinds could be integers (1, 2, 3 etc) or fractions (equation, equation, equation) or irrational numbers (equation, equation).

Solving For X

The most difficult part of algebra might be solving an equation for a variable or solving for x as it is often called. For these problems, you are given an equation, or you might have to construct an equation based on a text problem. This equation contains a variable, often called x. If x has a certain value, the equation is true, so the left hand side equals the right hand side. The goal of these problems is to solve the equation for x to find the value of x. To do this, you need to have a good understanding of the basic operations. Then you can transform the equation by applying those basic operations to both sides of the equation until x is isolated on one side.

Algebra Study Guide

We cover some of the most difficult topics of algebra in the algebra category. If you have questions or if you can’t find the topic you are looking for, please use the feedback button below. Further information to guide your algebra studies can be found at