Solving one-step equations
Use this page when you want the cleanest beginner route into equation solving before moving on to longer algebra questions.
Start here if you want the short version before reading the full method.
- A one-step equation needs only one inverse operation to isolate the variable.
- Use the opposite operation of what is happening to the variable.
What this topic means and what to look for first.
One-step equations are useful because they show the basic logic of solving without extra algebra clutter.
If this stage feels automatic, two-step and multi-step equations become much easier to manage.
One reliable route through the topic.
- 1Identify the single operation acting on the variable.
- 2Choose the inverse operation that undoes it.
- 3Apply that inverse operation to both sides.
- 4Check the result in the original equation.
See the method in action.
x + 7 = 12
- Subtract 7 from both sides.
- This gives x = 5.
- Check: 5 + 7 = 12.
x - 4 = 9
- Add 4 to both sides.
- This gives x = 13.
- Check: 13 - 4 = 9.
3x = 15 and x/5 = 3
- For 3x = 15, divide both sides by 3 to get x = 5.
- For x/5 = 3, multiply both sides by 5 to get x = 15.
- In both cases, the inverse operation isolates x immediately.
Things that commonly send the method off track.
- Using the wrong inverse operation.
- Changing one side of the equation but not the other.
- Rushing the arithmetic when the question looks too easy.
Use a short verification pass before moving on.
- Substitute the final value back into the original equation.
- Make sure the original left side really becomes the original right side after the substitution.
Try a few variations before switching to a calculator or solver tool.
- x + 9 = 15
- x - 6 = 10
- 4x = 28
- x/3 = 8
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Extra algebra revision resources
If you want more printed algebra practice after this page, these broader searches are a sensible next step.
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Algebra workbook and revision book search
Useful if you want more equation, factorising, and worked-example practice in one printed source.
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GCSE algebra practice resources search
A wider GCSE-style search if you want more mixed algebra questions beyond one online guide.
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Short answers worth checking.
It is an equation that needs only one inverse operation to isolate the variable.
Use the opposite of the operation acting on the variable: subtract for addition, add for subtraction, divide for multiplication, and multiply for division.
Substitute the value back into the original equation and see whether both sides match.
Continue with the next closely related topic.
Use the public site structure first, then switch into the solver tool only if you need a direct test.
CureMath uses artificial intelligence to suggest how a maths problem could potentially be solved. AI can make mistakes.
Check important answers independently before relying on them.