📘 Lesson 1 of 10 · Pre-Algebra

🔤 Variables

A variable is a letter that stands in for a number we don't know yet, or a number that can change. Variables are what let math describe patterns instead of just single facts.

Course progress: 10%

01 Key Concepts

What is a Variable?

A symbol, usually a letter like x, y, or n, used to represent an unknown or changing quantity.

Constants

Fixed values that don't change, like the numbers 2, 7, or -3 in an expression.

Substituting Values

Replacing a variable with a specific number to evaluate an expression, e.g., if x=3, then x+5 becomes 3+5=8.

Variables in Real Life

Variables model real, changing quantities: let d = distance traveled, or let p = price of an item.

Coefficients

The number multiplied directly in front of a variable, such as the 4 in 4x.

02 Solved Examples

Example 1 If x = 5, evaluate the expression x + 8.
  1. Substitute x with 5: 5 + 8.
Answer: 13
Example 2 If y = 4, evaluate 3y - 2.
  1. Substitute y with 4: 3(4) - 2.
  2. Multiply first: 12 - 2.
Answer: 10
Example 3 A taxi charges a flat $3 fee plus $2 per mile (m). Write an expression for the total cost, and find the cost for a 5-mile trip.
  1. Expression: total cost = 3 + 2m.
  2. Substitute m=5: 3 + 2(5) = 3 + 10.
Answer: Expression: 3 + 2m. Cost for 5 miles = $13

03 Practice Questions

1If x = 6, evaluate x + 10.
16
2If y = 2, evaluate 5y.
10
3If n = 7, evaluate n - 4.
3
4What is the coefficient in the term 9x?
9
5Write an expression for 'a number n plus 5'.
n + 5

📄 Variables — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.