Introduction to Algebra

Welcome to Algebra! You might feel nervous, but don’t worry—we’ll take this one step at a time and keep everything simple. 

What is Algebra? Algebra is a way of using letters (like x or y) to represent unknown numbers.
We do this all the time in real life without realizing it.

“If I have $20 and I spend x dollars, how much do I have left?”
That’s algebra! You're using a letter to stand in for a number.

What is a Variable? A variable is a letter representing a number we don’t know yet. The most common variables are x, y, and z.

Example:  x + 5
Here, x is the variable. It means we don’t know what number it is—yet!

What is an Algebraic Expression? An algebraic expression is a mathematical phrase that includes: 

• Numbers (like 5, 2, 10)
  Variables (like x or y)
  Math operations (like +, −, ×, ÷)
  
  
  

• ✅ Examples of Algebraic Expressions:

• x + 3

• 2y − 1

• 4a × 2
  
  
  

• These are not full equations yet because they don’t have an equal sign (=). They’re just parts of a math sentence.

• How Do You Evaluate an Expression?

• To evaluate means to find the value by plugging in a number for the variable.

• Example 1: x + 5, if x = 3

• ➡️ Plug in 3 for x: 3 + 5 = 8

• ✅ Final answer: 8

• How Do You Simplify an Expression?

• To simplify means to combine like terms or perform operations to make the expression shorter or cleaner.

• Example 2: 2x + 3x

• Since both terms have x, you can combine them:  2x + 3x = 5x

• ✅ Final answer: 5x

• Example 3: 4x − x

• This is like saying 4 apples minus 1 apple:   4x − x = 3x

• ✅ Final answer: 3x

• 🧠 Tip to Remember: Only combine like terms: same variable, same exponent

Algebra is just a way to organize your thinking. Don’t get scared by the letters—treat them like puzzles, and you’ll see how much fun this can be!