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.
- Substitute x with 5: 5 + 8.
Answer: 13
Example 2 If y = 4, evaluate 3y - 2.
- Substitute y with 4: 3(4) - 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.
- Expression: total cost = 3 + 2m.
- 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.