What is “Algebra?”

Algebra is defined as “the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations.”*

Simply put, Algebra is math that uses letters (often x and y) to represent unknown values. So, what does Algebra look like?

Below is an example of an algebraic equation:

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Seems simple enough, right? Here’s another:

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If I were to tell you that in both equations, x is equal to 2, would you believe me? You can probably tell just by looking at the first equation that x equals 2 without doing any math. However, the second equation requires a little more work before you can show that x in this case is also equal to 2.

These examples prove what you may already know: that Algebra starts out simple, but quickly becomes very complex. In order to solve these more complex equations, Algebra relies on a mathematical ruleset. And the foundation of this ruleset is built on the equals sign.

What is the equals sign?

The equals sign indicates balance, which must be maintained no matter what manipulation is performed on the equation. You may square an equation, subtract 10,000, add 0.00001, and perform almost any other** mathematical operation you can think of—so long as it’s done to both sides of the equals sign.

In simpler terms, what’s done on one side must be done to the other. You can think of this concept like a set of scales, where the scale acts as the equals sign.

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When the equation starts out, the two sides are equal. In the picture above, we see that two squares equal six circles.

If we want to see how much one square weighs, we remove one square from the left side without removing anything on the right.

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The scale above shows what happens when we remove one square from the left. The scale, or the equals sign, is no longer balanced. This breaks the rules of mathematics.

To balance this particular scale, we must remove three circles from the right side.

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This scale is once again balanced, and we can clearly see that one square equals three circles.

So, what did we just show? Maintaining an equation’s balance is a crucial component of Algebra, a branch of mathematics that uses letters and symbols to describe relationships between known and unknown values. Algebra can become more complex the deeper you dive into the subject, but if you follow the mathematical ruleset you’ll be able to find the answer to the equation at hand.

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*Source: https://www.dictionary.com/browse/algebra

**Just please do not divide by zero! This is not allowed as the result is undefined.