In math, we often work with numbers we know. For example, $2 + 2 = 4$. But what if we don't know a number yet? Or what if we want to write a rule that works for any number?

This is where variables come in. A variable is a letter or symbol that acts as a placeholder for a value. Think of it like a labeled box. You can put different numbers in the box, but the label—the variable—stays the same.

We use variables to turn specific statements into general rules. Instead of just saying that a square with sides of length 3 has a perimeter of $3+3+3+3 = 12$, we can create a general formula for the perimeter of any square.

If we let the letter $s$ represent the side length, the perimeter is always $s+s+s+s$, or more simply, $4 \times s$. Now, no matter what the side length is, we have a rule that works.

A mathematical expression is a combination of numbers, variables, and operations like addition, subtraction, multiplication, and division. An expression doesn't have an equals sign; it just represents a value.

For example, $x + 7$ is an expression. It means "a number plus seven." The value of this expression depends entirely on the value of $x$. This process of building expressions is a core part of algebra.

Notice that in algebra, we often write multiplication by placing a number and a variable next to each other, like $3y$, instead of using a multiplication sign ($3 \times y$). This is to avoid confusion, since the letter 'x' is a very common variable.

Once you have an expression with a variable, you can find its value if you know what number the variable stands for. This is called substituting a value into the variable and then evaluating the expression.

Let's take our expression, $x + 7$. What is its value if $x = 3$?

To find out, we replace every instance of $x$ with the number 3.

Now it's just a simple arithmetic problem. $3 + 7 = 10$. So, when $x=3$, the expression $x+7$ evaluates to 10.

The power of this is that we can use the same expression for any value of $s$. If the side of our square was 10 inches ($s=10$), the perimeter would be $4 \times 10 = 40$ inches. If it was 2.5 feet ($s=2.5$), the perimeter would be $4 \times 2.5 = 10$ feet. The expression $4s$ is a general tool, and substitution is how we use it for a specific case.

Let's see what you've learned about variables and expressions.