In arithmetic, you work with numbers you know, like $2 + 2 = 4$. Algebra introduces a twist: what if you don't know one of the numbers? What if a value can change? Instead of leaving a blank space, we use a symbol as a placeholder. This is usually a letter, like $x$ or $y$.

Think of a variable as a box. You might not know what's inside, but you can still talk about it and move it around. For example, if you get paid $15 per hour, and $h$ represents the hours you work, your total pay is $15 \times h$. You don't know the exact amount yet, but you have a way to describe it.

When you combine variables, numbers (called constants), and arithmetic operations ($+, -, \times, \div$), you create an algebraic expression. It's like a mathematical phrase. An expression doesn't have an equals sign, so it doesn't state a complete relationship. It just represents a value.

In these examples, the numbers 7, 4, and 2 are often called coefficients when they are multiplied by a variable. A coefficient is simply the number in front of a variable.

An equation is a statement that two expressions are equal. It's like a perfectly balanced scale. What's on the left side of the equals sign has the exact same value as what's on the right side.

The equation $3x + 2 = 11$ tells us that the expression on the left, $3x + 2$, is equal to the expression on the right, $11$. The goal in algebra is often to find the value of the variable ($x$) that keeps the scale balanced.

Sometimes in life, things aren't perfectly equal. You might need at least $20 to buy a ticket, or you can spend no more than $50. These relationships are described using inequalities.

An inequality is a statement that compares two expressions that are not necessarily equal. It uses special symbols to show the relationship.

These building blocks—variables, expressions, equations, and inequalities—are the foundation of algebra. Understanding them opens the door to solving a huge range of problems.