What Is a Variable?
In algebra, a variable is a letter that stands in for a number we don’t know yet. Variables can be any letter, but common ones are x, y, or n.
For example, if we say:
x is the number of apples you have,
Then an expression like x + 3 means “the number of apples you have plus 3.”
Variables are important because they allow us to create general rules and patterns that apply to many situations.
What Is an Algebraic Expression?
An algebraic expression is a math phrase that includes:
- Variables
- Numbers
- Operations (like addition, subtraction, multiplication, or division)
Most importantly, an expression does not have an equal sign.
Examples of Algebraic Expressions:
x + 53y - 24a(which means 4 × a)m/3(which means m ÷ 3)
Example: 2x + 7
xis the variable (an unknown number)2is the coefficient7is a constant
This expression means “two times a number, plus seven.”
What Is an Equation?
An equation is a math statement that shows two things are equal. It always includes an equals sign (=).
Examples of Equations:
x + 3 = 72y = 105a - 4 = 16
In each equation, your goal is to solve for the variable. This means you’re trying to figure out which number makes the equation true.
Example: Solve x + 3 = 7
- Subtract 3 from both sides:
x = 4
Check: 4 + 3 = 7 ✅ True!
Simplifying Algebraic Expressions
Sometimes algebraic expressions look complicated. But we can simplify them by combining like terms.
Like terms are terms that have the same variable raised to the same power.
Example 1: Simplify 4x + 3x
4x + 3x = 7x
Example 2: Simplify 5y - 2 + 3y + 6
5y + 3y = 8y-2 + 6 = 4
Answer: 8y + 4
Example 3: Simplify 2x + 4 - x + 1
2x - x = x4 + 1 = 5
Answer: x + 5
Summary of Key Terms
| Term | Meaning |
|---|---|
| Variable | A letter that stands for an unknown number (like x, y) |
| Coefficient | A number multiplied by a variable (like 3 in 3x) |
| Constant | A fixed number that doesn’t change (like 5 in x + 5) |
| Expression | A combination of numbers, variables, and operations (no equal sign) |
| Equation | A math sentence showing two expressions are equal (has an = sign) |
| Like terms | Terms with the same variable and exponent (like 4x and 2x) |
Wrapping Up
Now you’ve learned how algebraic expressions work, how to simplify them, and how equations help us solve for unknown values. You’ve also seen how variables let us write general rules and represent real-world situations in math form.
But what happens when those equations follow a clear, predictable pattern—like a straight line on a graph?
In the next article, we’ll explore Linear Equations—a special kind of equation that shows a constant relationship between two variables. You’ll learn how to recognize them, solve them, and understand how they appear on a graph.
Get ready to connect algebra with geometry and dive deeper into the world of linear relationships!