How to solve linear equations
Use this guide to review the main route for linear equations before trying your own expression in CureMath — AI Math Explainer.
Start here if you want the short version before reading the full method.
- To solve a linear equation, isolate the variable by undoing the operations in reverse order.
- Keep the equation balanced by doing the same operation to both sides every time.
What this topic means and what to look for first.
This page is the general solving overview for linear equations, so it is designed to show the recurring pattern before you move into one specific subcase.
The goal is not only to reach the final value, but to keep each line easy to justify and easy to check.
One reliable route through the topic.
- 1Identify the operations acting on the variable.
- 2Undo outer addition or subtraction first where needed.
- 3Undo multiplication or division next.
- 4If brackets or fractions appear, simplify them before trying to isolate the variable fully.
- 5Check the final value in the original equation.
Choose the route that fits the quadratic.
Use it when one inverse operation is enough to isolate the variable.
Use it when you need to undo an outer addition or subtraction before a multiplication or division step.
Use it when brackets, fractions, or decimals need simplifying before the usual pattern becomes obvious.
See the method in action.
x + 5 = 17
- Subtract 5 from both sides.
- So x = 12.
- Check by substitution: 12 + 5 = 17.
3x - 4 = 11
- Add 4 to both sides to get 3x = 15.
- Divide by 3.
- So x = 5.
2(x + 3) = 14
- Expand first to get 2x + 6 = 14.
- Subtract 6 to get 2x = 8.
- Divide by 2, so x = 4.
Things that commonly send the method off track.
- Undoing the multiplication before clearing the addition or subtraction around the variable.
- Applying an operation to one side only.
- Forgetting to expand the bracket before treating the equation like a simpler form.
Use a short verification pass before moving on.
- Substitute the final value into the original equation, not just a simplified intermediate line.
- If the check fails, go back to the first transformation where the structure of the equation changed.
Try a few variations before switching to a calculator or solver tool.
- x - 8 = 14
- 4x + 3 = 19
- 5(x - 1) = 20
- x/4 + 6 = 9
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Extra algebra revision resources
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Short answers worth checking.
Undo the operations acting on the variable in reverse order while keeping both sides of the equation balanced.
It means getting the variable on its own so the equation directly shows its value.
Put the value back into the original equation and make sure both sides match exactly.
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.