## Algebra

Algebra is a branch of math that performs a magic trick – it takes something that’s unknown and – poof! – turns it into something known. Algebra does this by:

- using letters (variables) to stand for mystery numbers, and
- giving you a process to let you discover the value of the variables.

In algebra, a letter is often used to stand for a number. The letter used to stand for a number is called a variable. You can use any letter, but a, b, c, n, x, y, and z are the most commonly used letters. In the following sentences, different letters are used to stand for numbers.

- x + 3 = 5 (x is a variable)
- a – 2 = 6 (a is a variable)
- y / 3 = 4 (y is a variable)
- 5z = 10 (z is a variable)
- x + y = 7 (Both x and y are variables)

When you use a letter to stand for a number, you don’t know what number the letter represents. Think of the letters x, a, y, and z as mystery numbers.

A variable can be part of an expression, an equation, or an inequality. A mathematical expression is part of a mathematical sentence, just as a phrase is part of an English sentence. Here are a few examples of mathematical expressions: 3x, x + 5, x – 2, x / 10. In each of these expressions it is impossible to know what x is. The variable x could be any number.

Mathematical expressions are named based on how many terms they have. A monomial expression has one term.

- x is a monomial expression.
- 3 is a monomial expression.
- z is a monomial expression.
- 6x is a monomial expression.

A binomial expression has two unlike terms combined by an addition or subtraction sign.

- x + 3 is a binomial expression.
- a – 4 is a binomial expression.
- x + y is a binomial expression.

A trinomial expression has three unlike terms combined by addition and/or subtraction signs.

- x + y – 3 is a trinomial expression.
- 2x – 3y + 7 is a trinomial expression.
- 4a – 5b + 6c is a trinomial expression.

A polynomial expression has two, three, or more unlike terms combined by addition and/or subtraction signs. Binomials and trinomials are polynomial expressions. The following are also polynomial expressions;

- x + y + z – 4 is a polynomial expression.
- 2a + 3b – 4c + 2 is a polynomial expression.

A mathematical sentence contains two mathematical phrases joined by an equals sign or an inequality sign. An equation is a mathematical sentence in which the two phrases are joined by an equals sign. Notice that the word equation starts the same way as the word equal.

- 3 + 6 = 9 is an equation
- x + 1 = 2 is an equation
- 7x = 14 is an equation
- 0 = 0 is an equation
- 4x + 3 is not an equation. It does not have an equals sign. It is a mathematical expression.

Some equations are true and some equations are false.

- 3 = 2 + 1 is a true equation.
- 3 + 5 = 7 is an equation, but it is false.
- 1 = 5 is also an equation, but it is also false.
- x + 1 = 5 is an equation. It could be true or it could be false.

Whether x + 1 = 5 is true of false depends on the value of x. If x is 4, the equation x + 1 = 5 is true. If x = 0, x + 1 = 5 is false. If x is any number other than 4, the equation x + 1 = 5 is false.

An inequality is a mathematical sentence in which two phrases are joined by an inequality symbol. The inequality symbols are greater than, “>”; greater than equal to, “>=”; less than, “<“; and less than equal to, “=<“. Six is greater than five is written as 6 > 5. Seven is less than ten is written as 7 < 10.

All in all, Algebra gives you power. Algebra gives you the power to move on to bigger and better things in mathematics. Algebra gives you the power of knowing that you know something that your neighbor doesn’t know. Algebra gives you the power to be able to help someone else with an algebra task or to explain to your child about these logical mathematical processes. Algebra is a system of symbols and rules that is universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end. It’s an organizational tool that is most useful when followed with the appropriate rules.

From here you may want to:

- Read the definition of algebra
- Find books on algebra