How to Learn Algebra in Easy Steps

By Jacob Nomi; Updated April 24, 2017
Algebra can be fun.

Algebra intimidates many people, but algebra is nothing more than an extension of the basic arithmetic you use every day. Algebra is easy if you consider the basic rules as your magic bag of tricks. The rules become automatic if you do a lot of practice exercises. Then when you encounter a problem, you'll know which tricks, or rules, you'll need to solve the algebraic problem.

Review your basic arithmetic and mathematics. Even if you remember what negative numbers are or how to add fractions, doing practice sets can be a refresher and confidence booster. Courses and textbooks exist that cover pre-algebra, which is an intensive review and introduction to the basics.

Then take the plunge. In algebra, the basic operations are still performed but there are letters as well as numbers in the equations. These letters are known as variables. Many of the problems you will face in algebra are concerned with finding the value of a given variable.

For example, solve for x: 4x + 6x + 12 = 22. First combine the like terms (terms that have the same variable). In this problem, these like terms are 4x + 6x: 10x + 12 = 22. Next, isolate the variable since you are solving for that term by adding -12 to each side of the equation: 10x + 12 - 12 = 22 - 12. Basic addition and subtraction yields: 10x = 10. Remember that multiplying a number by its reciprocal makes it a one? That's how you solve this: (1/10)10x = 10(1/10) yielding x = 1.

Similar principles apply for multiplication in algebra. Multiply these terms: x ( 3x + 5 + 6). You first combine the like elements in the parentheses: x( 3x + 11) and now you multiply each term within the parentheses by x: 3x² + 11x. Variables are multiplied just as numbers are: 2 times 2 equals 4 or 2², x times x equals x².

In the last step you multiplied two terms to get the solution (3x² + 11x). x and (3x + 11) are referred to as factors of the solution. Factoring is used in algebra to break down what seem to be complex problems. By breaking them down into smaller pieces, you can apply your math skills to find the answers.

When you are asked to factor an equation such as: x² + 5x = 0, you look for common elements in each term of the equation. Here x is a common element, as (x² = x times x) and (5x = 5 times x). You extract that common element to get: x(x + 5) = 0. There's an easy way to get the final answer here.

The equation indicates that the two factors here, when multiplied, become 0. Remember that any number times zero equals zero. So, one solution is that x = 0: 0(0 + 5) = 0. There is another solution you can find in the (x + 5) factor. To make that a zero, you substitute -5 for x: -5(-5 + 5)= -5(0) = 0. x can equal either 0 or 5 which are the solutions to the problem. That's all there is to getting started in algebra. Review your math skills, practice and start filling up that magic bag of tricks.


Find sites on the internet that have interactive drills, the instant feedback is great for honing your skills. When you have free time, try doing some simple math exercises for fun, as you would do a crossword or other puzzle.


Remember you can only add or subtract like terms, x and x² are not like terms as they have different values. When you are factoring, however, you can break down multiples like x² and factor them out as in: x² + 3x = x(x + 3). Addition and factoring are different types of operations and should not be confused.

About the Author

Jacob Nomi has been writing professionally since 2011. His areas of expertise include linguistics, law, Russian literature, exercise science and nutrition. Nomi holds a Master of Arts in Russian literature and linguistics from the State University of New York at Stony Brook.