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How to solve for x, step by step
Solving for x just means finding the number that x stands for. The secret: whatever you do to one side, do to the other side too.
Think of a balance scale
An equation is like a balance. The left side and the right side weigh the same. If you take 3 away from one side, you must take 3 away from the other side, or it tips over.
One-step equations
Undo what's happening to x by doing the opposite.
x + 5 = 12
5 is being added to x, so subtract 5 from both sides: x + 5 − 5 = 12 − 5, so x = 7.
4x = 20
x is being multiplied by 4, so divide both sides by 4: x = 5.
| If x is… | Undo it by… |
|---|---|
| plus a number | subtracting it |
| minus a number | adding it |
| times a number | dividing by it |
| divided by a number | multiplying by it |
Two-step equations
Undo the adding or subtracting first, then the multiplying or dividing.
- Start with: 3x + 4 = 19
- Subtract 4 from both sides: 3x = 15
- Divide both sides by 3: x = 5
- Check it: 3 × 5 + 4 = 15 + 4 = 19. ✓ It works!
Try one yourself
2x − 6 = 10
Hint: what's happening to 2x? Undo that first, then deal with the 2.
Common mistakes
- Only changing one side. Both sides always get the same change.
- Undoing in the wrong order. Adding and subtracting come off first.
- Skipping the check. Putting your answer back in takes ten seconds and catches most mistakes.
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