Solve for the unknown (like x)
Imagine an equation is a balance scale. Whatever you do to one side, you must do to the other side so the scale stays balanced. The unknown (often called x) is a number that we need to find.
Step-by-step rules
- Find the unknown: Look for the variable (like x).
- Use inverse operations: To undo adding, subtract. To undo subtracting, add. To undo multiplying, divide. To undo dividing, multiply.
- Do the same to both sides: Whatever you do on one side of the =, do it on the other side too.
- Check by putting your answer back into the original equation.
Examples
1) x + 5 = 12
We want x alone. Undo +5 by subtracting 5 on both sides:
x + 5 - 5 = 12 - 5
x = 7
Check: 7 + 5 = 12 ✅
2) x - 4 = 9
Undo -4 by adding 4 on both sides:
x - 4 + 4 = 9 + 4
x = 13
Check: 13 - 4 = 9 ✅
3) 3x = 15
Here x is multiplied by 3. Undo ×3 by dividing both sides by 3:
3x ÷ 3 = 15 ÷ 3
x = 5
Check: 3 × 5 = 15 ✅
4) x / 4 = 6
Undo ÷4 by multiplying both sides by 4:
(x / 4) × 4 = 6 × 4
x = 24
Check: 24 ÷ 4 = 6 ✅
5) Two-step: 2x + 3 = 11
First undo +3 by subtracting 3 from both sides:
2x + 3 - 3 = 11 - 3 → 2x = 8
Now undo ×2 by dividing both sides by 2:
2x ÷ 2 = 8 ÷ 2 → x = 4
Check: 2×4 + 3 = 8 + 3 = 11 ✅
Quick tips
- Always keep the equation balanced — do the same thing to both sides.
- Work step by step. Don't try several things at once.
- Check your answer by putting it back into the original equation.
Practice problems (try these)
- x + 6 = 10
- x - 7 = 5
- 4x = 20
- x / 5 = 3
- 3x + 2 = 11
Answers
- x = 4
- x = 12
- x = 5
- x = 15
- x = 3
If you want, give me one of your equations and I'll show you how to solve it step by step!