VIDEO: Brief Review: Representing a Variable Algebraically

What Is a Variable?

A variable is a symbol, usually a letter, that can stand for different things. Let’s look at some examples.

• The Unknown. Remember when you first learned to add numbers? You probably saw “missing addend” problems like this:

In this example the box represents an unknown value. It could also be replaced by a letter.

In this example the letter x represents the unknown value. While x can take on different values, there is only one value for x that makes this equation true.

• An Input Value. Many equations, functions, and formulas use variables to represent numbers. Look at this example.

By substituting different values for x, you can evaluate this function. Here are some examples. 

What Is an Expression?

A mathematical expression can include numbers, variables, and operation symbols. Let’s start with the simplest type of expression, a numerical expression.

Numerical Expressions

A numerical expression includes numbers and operations. Here are some examples.

When a numerical expression includes operation symbols, the expression can often be simplified. These equations show an expression on the left and its simplified form on the right. 

Algebraic Expressions

An algebraic expression includes numbers, variables, and operation symbols. An algebraic expression can look like a polynomial. Here are some examples.

Algebraic expressions are sometimes referred to as variable expressions.

Evaluating Algebraic Expressions

Because algebraic expressions include variables, sometimes you can replace the variable with a specific value for the variable. In such a case, you are left with a numerical expression. Here is an example:

For the expression 2x + 4, let x = 3. Here is the result:

The numerical expression on the right can be simplified.

In this Brief Review, we look at how to represent variables algebraically.

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