Solving One-Step Equations
By the end of this page, you will be able to solve any one-step equation — and explain why your method works.
The Big Idea
An equation is like a balance scale. The two sides of x + 7 = 12 weigh exactly the same. If you add, subtract, multiply, or divide on one side, you must do the same thing to the other side — or the scale tips and the equation is no longer true.
Your goal is always the same: get x alone on one side. To do that, you “undo” whatever is being done to x by using the inverse (opposite) operation.
Example 1: An addition equation
Solve x + 7 = 12. Something is being added to x, so you undo it by subtracting.
| Equation | What you do | Why |
|---|---|---|
| x + 7 = 12 | Look at what is happening to x | 7 is being added to x |
| x + 7 − 7 = 12 − 7 | Subtract 7 from both sides | Subtracting undoes the +7 and gets x alone. Both sides stay balanced. |
| x = 5 | Done! | Check: 5 + 7 = 12 ✓ |
Example 2: A subtraction equation
Solve x − 4 = 9. Something is being subtracted from x, so you undo it by adding.
| Equation | What you do | Why |
|---|---|---|
| x − 4 = 9 | Look at what is happening to x | 4 is being subtracted from x |
| x − 4 + 4 = 9 + 4 | Add 4 to both sides | Adding undoes the −4 and gets x alone. |
| x = 13 | Done! | Check: 13 − 4 = 9 ✓ |
Example 3: A multiplication equation
Solve 3x = 15. Remember: 3x means “3 times x“. You undo multiplying by dividing.
| Equation | What you do | Why |
|---|---|---|
| 3x = 15 | Look at what is happening to x | x is being multiplied by 3 |
| 3x 3 = 15 3 | Divide both sides by 3 | Dividing undoes the “times 3” and gets x alone. |
| x = 5 | Done! | Check: 3 × 5 = 15 ✓ |
Example 4: A division equation
Solve x 2 = 6. Here x is being divided by 2, so you undo it by multiplying.
| Equation | What you do | Why |
|---|---|---|
| x 2 = 6 | Look at what is happening to x | x is being divided by 2 |
| x 2 × 2 = 6 × 2 | Multiply both sides by 2 | Multiplying undoes the “divided by 2” and gets x alone. |
| x = 12 | Done! | Check: 12 ÷ 2 = 6 ✓ |
⚠ Watch out for these common mistakes
- Changing only one side. If you subtract 7 on the left but not the right, the “scale” tips and the equation is broken. Both sides, always.
- Using the same operation instead of the inverse. To solve x + 7 = 12, you subtract 7 — you don’t add more. Ask yourself: “What undoes what is being done to x?”
- Forgetting to check. Put your answer back into the original equation. If both sides match, you know you’re right — no guessing needed.
Quick reference: which inverse do I use?
| If the equation shows… | Undo it by… |
|---|---|
| Addition, like x + 7 | Subtracting from both sides |
| Subtraction, like x − 4 | Adding to both sides |
| Multiplication, like 3x | Dividing both sides |
| Division, like x ÷ 2 | Multiplying both sides |
Ready to practice? Head to the quiz below. For every problem, follow the same three steps: look at what’s happening to x, undo it on both sides, and check your answer.