Maths · Algebra Foundations
One-step equations
Solve x + 4 = 12 style equations.
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What is a One-Step Equation?
An equation is like a balanced scale. Both sides have the same value. A one-step equation needs just one operation to solve. For example, x + 4 = 12 means a number plus four equals twelve.
The Golden Rule: Keep It Balanced
Whatever you do to one side, do to the other side too. This keeps the equation balanced. Think of it like a seesaw that must stay level.
Solving Addition Equations
To solve x + 4 = 12, we need x on its own. Subtract 4 from both sides. On the left, +4 and −4 cancel out. We get x = 8.
Using Inverse Operations
Inverse operations are opposites. Addition and subtraction are inverses. Multiplication and division are inverses too. We use the inverse to 'undo' what is happening to x.
Check Your Answer
Always substitute your answer back into the original equation. If both sides equal the same number, you solved it correctly! For x = 8: does 8 + 4 = 12? Yes!
Worked examples
1. Solve x + 7 = 15
- We need x alone, so subtract 7 from both sides.
- x + 7 − 7 = 15 − 7
- x = 8
- Check: 8 + 7 = 15 ✓
2. Solve x + 3 = 10
- Subtract 3 from both sides to isolate x.
- x + 3 − 3 = 10 − 3
- x = 7
- Check: 7 + 3 = 10 ✓
3. Solve x + 9 = 20
- Use the inverse of adding 9, which is subtracting 9.
- x + 9 − 9 = 20 − 9
- x = 11
- Check: 11 + 9 = 20 ✓
Try it yourself
Solve x + 6 = 14
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