Solve for x: Algebra Basics
Algebra sounds scary, but solving for x is just undoing what's been done to it. Learn the one rule that makes it all work.
x is just a mystery number
An equation says two things are equal. The letter (often x) stands for a number you don't know yet. “Solving” means finding the number that makes the equation true.
You can guess small ones like this. The method below works for any equation, including ones you can't guess.
The balance rule
Think of an equation as a balanced scale. You can do anything to one side, as long as you do exactly the same to the other. It stays balanced.
Your goal is to get x on its own on one side. To remove something, do the opposite:
| If x has… | Do this to both sides |
|---|---|
| + 7 | subtract 7 |
| − 4 | add 4 |
| × 3 (written 3x) | divide by 3 |
| ÷ 2 (written x/2) | multiply by 2 |
Two-step equations
When x has two things done to it, undo them in reverse: add or subtract first, then multiply or divide.
- Subtract 5 from both sides: 3x = 15
- Divide both sides by 3: x = 5
- x = 5
- Add 2 to both sides: x/4 = 5
- Multiply both sides by 4: x = 20
- x = 20
Always check your answer
Put your answer back into the original equation. If both sides match, you're right.
- 3 × 5 + 5 = 15 + 5 = 20
- 20 = 20 ✓
x on both sides? Move all the x terms to one side first. For 5x + 2 = 3x + 10: subtract 3x from both sides to get 2x + 2 = 10, then solve as normal (x = 4).
Solve a·x + b = c. Change the numbers and watch the steps.