At its core, algebra is a way to work with unknown quantities. Instead of just using numbers like 2, 10, or -5, we use letters to stand in for numbers we don't know yet. These letters are called variables.

The numbers that don't change are called constants. They have a fixed value. In the expression $2x + 3$, the number 3 is a constant. It's always 3.

Let's break down a typical expression: $4x - 7$.

This expression is made of parts, called terms, separated by addition or subtraction signs. This one has two terms: $4x$ and $-7$.

The number multiplied by a variable is its coefficient. In the term $4x$, the coefficient is 4. It tells us we have four $x$'s. A variable by itself, like $y$, has an invisible coefficient of 1.

We can translate everyday language into algebraic expressions. For example, if we want to represent "ten dollars more than the price of a ticket," we could write it as $p + 10$, where $p$ is the variable representing the ticket price.

What about "the cost of four coffees"? If one coffee costs $c$, then four would be $4c$.

Often, expressions are longer than they need to be. We can simplify them by combining like terms. Like terms are terms that have the exact same variable parts, meaning the same letters raised to the same powers. The coefficients can be different.

For example, $3x$ and $5x$ are like terms. So are $8y^2$ and $-2y^2$. However, $3x$ and $3y$ are not like terms, because their variables are different.

To simplify, you just add or subtract the coefficients of the like terms and keep the variable part the same. Think of it like sorting fruit: you can combine three apples and five apples to get eight apples, but you can't combine three apples and two oranges.

Sometimes you'll see a number outside a set of parentheses, like $3(x + 5)$. This means you need to multiply the number outside by every term inside the parentheses. This is called the distributive property.

So, for $3(x + 5)$, we distribute the 3:

1. Multiply 3 by $x$ to get $3x$.
2. Multiply 3 by 5 to get 15.

The result is $3x + 15$. This also works with subtraction. For example, $4(2y - 1)$ becomes $4(2y) - 4(1)$, which simplifies to $8y - 4$.

Expressions are useful because we can evaluate them. This means finding their numerical value once we know what the variables stand for. To do this, we substitute the given number for the variable and perform the arithmetic.

Let's evaluate the expression $2a + b - 4$ if we know that $a=5$ and $b=3$.

Let's try one more. Evaluate $5(x-2) + y$ for $x=4$ and $y=1$.

First, substitute the values: $5(4-2) + 1$. Next, handle the parentheses: $5(2) + 1$. Then, multiply: $10 + 1$. Finally, add: $11$.

Understanding these basic rules for building, simplifying, and evaluating expressions is the first major step into the world of algebra. These skills form the foundation for solving much more complex problems.