Variables and Equations

1-3Equations

Overview

An equation says two expressions are equal. A solution is a value of the variable that makes the equation true.

Key ideas

  • ‘=’ separates two equal expressions.
  • Check a proposed solution by substitution.
  • Some equations have no solution; some have many.

Worked examples

Example 1

Problem. Is 4 a solution of x + 3 = 7?

Solution. 4 + 3 = 7 ✓ Yes.

Example 2

Problem. Solve mentally: n − 5 = 12.

Solution. n = 17

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Is 6 a solution of 2x − 1 = 11?

  2. 2.

    Solve mentally: 3y = 21.

  3. 3.

    Solve mentally: x/4 = 5.

Challenge problems

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

  1. 1.

    Is x = −2 a solution of 3x + 7 = 2x + 5?

  2. 2.

    Find two solutions of |x| + 1 = 3.