In arithmetic, we work with numbers we know, like $5 + 3 = 8$. Algebra introduces a new idea: working with numbers we don't know yet. To do this, we use variables.

A variable is just a symbol, usually a letter like $x$ or $y$, that stands in for a number. Think of it as a labeled box. You might not know what's inside, but you know the box's name. We can move the box around and describe what we'll do with it once we know its contents.

Why bother with this? Variables let us write rules and solve problems for any number, not just one specific case. They give us a powerful way to describe relationships. For example, if you get paid $15 per hour, you can use a variable to represent the number of hours you work. This lets you create a rule to calculate your pay for any number of hours.

When we combine variables, numbers, and operations like addition, subtraction, multiplication, and division, we create an algebraic expression. It's like a set of instructions. For instance, the expression $x + 5$ tells us to take whatever number $x$ represents and add five to it.

In algebra, we often leave out the multiplication sign to avoid confusion with the letter $x$. So, if you see $2y$, it means $2 \times y$. If you see $ab$, it means $a \times b$.

One of the most important skills in algebra is translating everyday language into the language of math. This means turning a written phrase into an algebraic expression.

Just as we can translate words into expressions, we can also interpret what an expression means in a real-world context. This helps us understand the relationships it describes.

Imagine you're buying tickets to a concert. Each ticket costs $50, and there's a one-time service fee of $5. Let's use the variable $t$ to represent the number of tickets you buy.

The expression for the total cost would be $50t + 5$. What does this mean? It says to multiply the number of tickets ($t$) by $50, and then add the $5 service fee to find your total cost. If you buy 2 tickets, $t=2$, and the cost is $50(2) + 5 = 105$. If you buy 4 tickets, $t=4$, and the cost is $50(4) + 5 = 205$. The expression works for any number of tickets.

Being able to read and write these expressions is the first major step in mastering algebra. Now, let's check your understanding.

Great work. With variables and expressions, you now have the basic building blocks for exploring the world of algebra.