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. 1.

    Evaluate 2y − 1 when y = 6.

  2. 2.

    Evaluate 5a + 3b when a = 2, b = 4.

  3. 3.

    Write an expression for ‘twice a number n.’

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    If a = 3, b = 2, and c = 5, evaluate a² + 2bc − c.

  2. 2.

    Write an expression for the sum of a number n and twice another number m, divided by 3.