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.
Is 6 a solution of 2x − 1 = 11?
- 2.
Solve mentally: 3y = 21.
- 3.
Solve mentally: x/4 = 5.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Is x = −2 a solution of 3x + 7 = 2x + 5?
- 2.
Find two solutions of |x| + 1 = 3.