Variables and Equations
1-1Variables
Overview
A variable is a letter that stands for a number. Algebraic expressions combine variables, numbers, and operations.
Key ideas
- A variable represents an unknown or changing value.
- ‘3x’ means 3 times x; the multiplication sign is implied.
- Evaluate an expression by replacing the variable with a given number.
Worked examples
Example 1
Problem. Evaluate 4n + 5 when n = 3.
Solution. 4(3) + 5 = 12 + 5 = 17
Example 2
Problem. Write an expression for ‘a number x increased by 7.’
Solution. x + 7
Practice
Try each one. Click Show answer when ready.
- 1.
Evaluate 2y − 1 when y = 6.
- 2.
Evaluate 5a + 3b when a = 2, b = 4.
- 3.
Write an expression for ‘twice a number n.’
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
If a = 3, b = 2, and c = 5, evaluate a² + 2bc − c.
- 2.
Write an expression for the sum of a number n and twice another number m, divided by 3.