# Definition of Algebra

by Ron Kurtus (updated 18 January 2022)

Algebra is a branch of Mathematics that uses letters of the alphabet to represent objects, numbers or even groups of numbers or expressions. In many cases, algebra uses shorthand mathematical notation to simplify complex or very large terms.

When the letters are used to represent objects, the mathematics involved is very basic. Letters can also represent constant values for the sake of convenience. When the letters represent numbers or expressions, those letters are called variables, since they have no set value.

You can find the values of variables by solving an equation or set of equations containing those variables. Solving equations is an important part of algebra.

Questions you may have include:

• What is the algebra of objects?
• What are variables?
• How is an equation solved?

This lesson will answer those questions.

## Algebra of objects

A simple area of algebra concerns applying arithmetic to the combination of objects. You can perform arithmetic operations by substituting letters of the alphabet to represent objects.

For example, if you represent an apple with the letter "a", then three apples could be denoted by 3a.

Although your can add and subtract objects of the same type, you cannot multiply or divide them, and negative objects cannot exist.

## Constants and variables

Constants and and are represented by letters in the alphabet, as well as other symbols.

### Constants

A constant is a number that you have designated a letter for the sake of convenience. They are usually used in scientific formulas.

A good example is the constant pi, which is represented by the Greek letter π.

The value of pi is π = 3.14159.... It does not vary or change.

### Variables

A major part of algebra concerns dealing with unknown values called variables. This is as opposed to arithmetic, which is based entirely on known number values.

You can add, subtract, multiply, divide, find the square root, and apply other operations on variables.

## Solutions to equations

An equation consists of two mathematical expressions separated by an equals sign. It is a statement that the values of expressions are equal. Expressions are combinations of variables, numbers, and mathematical operations.

To find a solution to the equation, you perform operations on the left and right sides of the equal sign.

For example: 5x + 6 = 2x + 3 is an equation, where

• x is the variable
• 5x + 6 and 2x + 3 are expressions

Depending on the equation, there may be from one to several solutions. In this case, to find the solution:

5x + 6 = 2x + 3

Subtract 2x from both sides of the equals sign to get:

3x + 6 = 3

Subtract 6 from both sides of the equals sign:

3x = −3

Divide both sides by 3:

x = −3

## Summary

Algebra uses letters of the alphabet to represent objects, numbers or even groups of numbers or expressions.

When the letters are used to represent objects, the mathematics involved becomes very simple. When the letters represent numbers or expressions, those letters are called constants or variables, depending on their use.

You can find the values of variables by solving an equation or set of equations containing those variables. Solving equations is an important part of algebra.

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