Understanding Variables

In algebra, a variable is a symbol—often a letter like \( x \) or \( y \)—that represents a number. You can think of variables as placeholders for unknown values or values that can change.

Algebraic Expressions

An expression is a combination of numbers, variables, and mathematical operations (like +, −, ×, ÷). Expressions don't have an equals sign.

• \( 3x + 7 \)
• \( a^2 - 4b \)
• \( 2(x + 5) \)

Why Use Variables?

Variables help us write general mathematical rules and solve problems where some information is missing or can change.

Tips for Working with Expressions

• Combine like terms (e.g., \( 2x + 3x = 5x \))
• Use parentheses to show grouping
• Always pay attention to the order of operations

Real-World Connection

If you have \( n \) apples and you buy 5 more, the total is \( n + 5 \). That's an algebraic expression!