How to Check Your Algebra Work and Find the First Wrong Step

The short answer

To find the first wrong step, compare each line with the one directly above it, not with the final answer. Name the operation and ask whether the new equation keeps the same solutions. For an equation move, check both sides were treated equally; for simplification, check the expression stayed equivalent. The first pair that fails is where the work breaks.

The annoying algebra mistake is rarely sitting on the last line. More often, it is a dropped minus sign or a rushed bit of arithmetic three lines earlier. The final answer only inherits the damage.

That is why checking algebra from the bottom up is frustrating. You can stare at x = 3 for a full minute and learn nothing. The useful question is smaller: what changed between these two neighboring lines, and was that change allowed?

For an ordinary linear equation, the first wrong step is the earliest transition where the new line is not equivalent to the line above it. Everything before that point is still useful. Everything after it needs to be rebuilt from the last valid line.

A four-pass way to check algebra

1. Keep the original problem visible

Do not erase the question or cover it with scratch work. You will need the original equation for the final check. It also stops a copied sign or number from quietly becoming the new problem.

2. Compare only two lines at a time

Start with line 1 and line 2. Ignore the rest of the page. If that transition is valid, move to lines 2 and 3. This turns a vague search for “the mistake” into a series of small yes-or-no checks.

3. Say what changed

Give the move a plain name: distribute 2, combine constants, add 3 to both sides, divide both sides by 6. If you cannot describe the move, slow down. A mystery jump is hard to verify and easy to get wrong.

For equations, the balance matters. Adding or subtracting the same quantity on both sides keeps the same solutions. So does multiplying or dividing both sides by the same nonzero constant. Changing only one side usually breaks the equivalence.

4. Test the final value in the original equation

Substitution is a separate check. Replace the variable in the original equation with your answer, simplify the left and right sides independently, and compare them. Equal values mean the proposed answer satisfies the equation. Different values mean it does not.

This confirms whether the answer works. It usually does not tell you where the work first went wrong, which is why the line-by-line pass still matters.

Worked example: the mistake is in the middle

Suppose this is the work on the page:

1.  2(3x - 4) + 5 = 21
2.  6x - 8 + 5 = 21
3.  6x - 3 = 21
4.  6x = 18
5.  x = 3

Check the transitions in order.

• Line 1 → 2 is valid. Distributing 2 gives 6x - 8, while the + 5 remains.
• Line 2 → 3 is valid. The constants combine because -8 + 5 = -3.
• Line 3 → 4 is the first wrong step. Adding 3 to both sides should turn 6x - 3 = 21 into 6x = 24, not 6x = 18.

The next step, 6x = 18 to x = 3, is internally consistent. That does not rescue the work. It is a valid move performed on an equation that was already broken.

Substitution catches the bad result:

Original:  2(3x - 4) + 5 = 21
Try x = 3
Left:      2(9 - 4) + 5 = 15
Right:     21
Result:    15 ≠ 21

Repair the work from line 3 instead:

6x - 3 = 21
6x = 24
x = 4

Now the original left side becomes 2(12 - 4) + 5 = 21. The answer checks.

The places algebra work usually breaks

These are worth checking first, but do not assume one of them must be the culprit.

• Distributing a negative. In -(x - 4), both terms change sign, so the result is -x + 4.
• Combining unlike terms. 3x + 2 cannot become 5x; one term has a variable and the other does not.
• Changing one side only. If you add 7 to isolate the variable, add 7 to both sides of the equation.
• Losing a sign while moving terms. “Moving” is shorthand. Write the actual addition or subtraction on both sides when signs feel slippery.
• Plain arithmetic. Sometimes the algebra is fine and -8 + 5 is where the page goes off course.

One practical habit helps with all five: write one meaningful change per line. Shorter work is not always clearer work.

How Math Solver checks your steps

Math Solver’s Check My Work tool appears after you solve a supported problem. Enter 2–12 typed lines in the order you wrote them. The checker compares neighboring lines and looks for the first transition it can prove invalid.

Treat inconclusive literally. It is not a quiet way of saying “correct.” It means the checker could not prove that transition valid or invalid. Keep reviewing the step, especially if it uses a rule outside the current supported scope.

This guide focuses on ordinary one-variable algebra, especially linear equations. Math Solver currently supports typed one-variable linear equations without variables in denominators, along with the other topics listed on the About page. It does not claim to check every kind of algebra.

Questions people ask

How do I find the first mistake in algebra?

Compare each line with the line immediately above it. Identify the operation, check that it was applied correctly, and stop at the first transition that changes the equation without a valid reason.

Is checking the final answer enough?

No. Substitution can show that an answer fails, but it usually cannot locate the step where the mistake began. Use substitution after the line-by-line check.

What does “inconclusive” mean in Check My Work?

It means Math Solver could not prove the step valid or invalid. It is not a correctness badge, and it should not be treated as one.

Can Math Solver check every algebra problem?

No. Check My Work is available after solving a supported problem and accepts 2–12 typed lines. Read how Math Solver verifies results and the current solve-for-x scope before relying on it for a new problem type.

If your final answer is the only thing you need to test, the next guide shows how to check a linear equation answer by substitution.

Sources

• OpenStax, “Verify a Solution of an Equation”
• OpenStax, “Division and Multiplication Properties of Equality”
• OpenStax, “Use a General Strategy to Solve Linear Equations”

Published and reviewed on October 7, 2026. We update this guide when the product scope changes.