Solving linear equations with decimals
Use this page when the decimal numbers make the equation feel messy and you want a cleaner route through it.
Start here if you want the short version before reading the full method.
- Decimal equations are often easier after you multiply through by 10, 100, or another sensible scale factor to remove the decimals first.
- Once the decimals are cleared, the equation usually becomes an ordinary linear-equation question.
What this topic means and what to look for first.
Decimals do not change the algebra logic, but they often make the arithmetic look heavier than it really is.
A quick scaling step can make the structure easier to read before you solve it normally.
One reliable route through the topic.
- 1Decide whether the decimal form is easy enough to keep or whether scaling would make the equation cleaner.
- 2If helpful, multiply both sides by the same power of 10 to remove the decimals.
- 3Solve the new linear equation using the usual isolate-the-variable routine.
- 4Check the final value in the original decimal equation.
See the method in action.
0.5x + 1 = 4
- Subtract 1 to get 0.5x = 3.
- Divide by 0.5.
- So x = 6.
0.4x + 1.2 = 3.6
- Multiply both sides by 10 to get 4x + 12 = 36.
- Subtract 12 to get 4x = 24.
- Divide by 4, so x = 6.
Things that commonly send the method off track.
- Multiplying only some terms when trying to clear decimals.
- Changing the scale on one side only.
- Treating 0.5x as if it meant x + 0.5 instead of 0.5 times x.
Use a short verification pass before moving on.
- Check the final value in the original decimal equation, not only in the scaled version.
- If you cleared decimals first, confirm that every term was scaled by the same amount.
Try a few variations before switching to a calculator or solver tool.
- 0.2x + 3 = 5
- 1.5x - 2 = 7
- 0.75x + 0.5 = 2.75
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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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A wider GCSE-style search if you want more mixed algebra questions beyond one online guide.
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Short answers worth checking.
Not always, but it often makes the arithmetic easier and the structure of the equation clearer.
Multiply every term on both sides by the same power of 10 so the decimals disappear consistently.
Substitute the value back into the original decimal equation and compare both sides directly.
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.