For students
How to find where you went wrong in a math problem
To find a mistake in your math, don’t redo the whole problem. Check your work one line at a time: each line should say the same thing as the line before it. The first line that doesn’t is where the mistake is — and it is usually a sign, a term that went missing, or the order of operations. Plug your answer back into the original problem to confirm it.
Updated October 9, 2026 · Published by MathSense AI (L8O LLC)
Check one line at a time
Every line of a solution is a promise: “this is equal to the line above.” A mistake breaks that promise once, and everything after it can look perfectly reasonable. That is why redoing the whole problem from scratch so often gives you the same wrong answer.
Check your answer first
Put your answer back into the original problem. If both sides don’t match, there is a mistake somewhere — now you know to look.
Compare each pair of lines
Cover everything except line 1 and line 2. Ask: did I do the same thing to both sides? Did every term make it across? Then move to lines 2 and 3.
Test a line with a number
Pick an easy value, like x = 1, and put it into two neighbouring lines. If they give different results, the mistake is between them.
Stop at the first broken line
Fix that line only, then redo the steps after it. The lines before it were right — keep them.
The slips to look for first
- A minus sign in front of brackets that reaches the first term but not the second: −3(x − 2) is −3x + 6, not −3x − 6.
- A term that disappears when you move things across the equals sign.
- Order of operations: 2 + 3 × 4 is 14, not 20.
- Doing something to one side of the equation but not the other.
- Copying a number wrong from one line to the next (a 6 becomes a 0).
- Dividing only part of one side: (6x + 4) ÷ 2 is 3x + 2, not 3x + 4.
Why it’s so hard to spot your own mistake
When you read your own work, you read what you meant to write, not what is on the page. That is normal — it happens to everyone, including teachers. Checking with a number, or having someone (or something) check each line for you, gets around it.
What it looks like with MathSense Tutor
You take a photo of the problem and your work. A math engine checks every line before the tutor says anything, so it can point to the exact line — then it asks you to fix it, instead of fixing it for you.
Illustrative example — simulated student work.
MathSense Tutor
Solve 4 − 3(x − 2) = 19
Student’s work:
4 − 3(x − 2) = 19
4 − 3x − 6 = 19
−2 − 3x = 19
−3x = 21
x = −7
My work — I got x = −7 but it doesn’t work when I check it
Tutor:
Engine-checked
Nice setup — and lines 3 to 5 follow correctly from line 2. The slip is in line 2, where you multiplied out the brackets. Look at the −3 and the −2 inside. What do you get when you multiply them?
Student: Asked for: Hint
Tutor:
Hint: a negative times a negative is positive. So −3 × (−2) = ?
Student: +6… oh. I wrote −6.
Tutor:
That’s the one. Fix line 2 and keep going — send me your steps and I’ll check every line.
Student’s work:
4 − 3x + 6 = 19
10 − 3x = 19
−3x = 9
x = −3
Redone
Tutor:
Engine-checked
Every line checks out: x = −3. And you found the fix yourself. Nice work. Want to make sure it sticks?
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How MathSense Tutor helps
“I can’t see which step is wrong.”
For arithmetic and algebra, a math engine checks every line of your work, so the tutor points to the exact line that slipped.
“I don’t want the answer, I want to get it.”
You get a question first, then a hint if you ask for one. The full solution is there only when you choose it.
“I’ll just make the same mistake on the next one.”
After you fix it, the tutor offers a similar problem so the fix sticks.
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Questions
- What is the most common mistake in algebra?
- Sign errors, especially a minus in front of brackets that only reaches the first term. Dropped terms and order-of-operations slips come next. Check those first when an answer doesn’t work.
- How do I check if my answer is right?
- Substitute it back into the original problem. If both sides are equal, the answer is right. If they aren’t, compare your lines in pairs to find the first one that changed the meaning.
- Can MathSense Tutor find my mistake from a photo?
- Yes. Take a photo of the problem and your handwritten work, or type it. For arithmetic and algebra, a math engine checks each line, and the tutor points to the line where the mistake is. For problems outside what the engine covers, the reply is labelled “tutor-reasoned”.
- Does it just tell me the right answer?
- No. It shows you where the mistake is and asks you to fix it, with a hint if you want one. You can always choose to see the full solution.