Math answer checker: substitute first, then compare a tool

What checking your own answer means

A check compares an answer with the problem it came from, so the method is to put the answer back and see whether it holds. The Mathway, QuickMath and Photomath pages we read describe solvers: you give the problem and the tool works it.

This page is about something narrower: you already have an answer and want to know whether it is right. That is a different job from asking a tool to work the problem, and the pages we read treat it differently. A Khan Academy lesson page, Symbolab’s algebra text and the University of Nebraska-Lincoln’s precalculus book describe checking by substitution. The tool pages describe how the tool solves, shows steps or graphs. For the solver side, with Photomath, OneNote and Wolfram|Alpha, and for a classroom trial of what a chat tool did to exam results, see our page on math solver apps.

Method: the statements about pages come from the pages as they read on 6 November 2026. The worked examples below are ours, and each one says so.

Check by putting the answer back

The Khan Academy page is a lesson on testing solutions to equations. Its description says the lesson tests different values for x to see which one satisfies the equation, and that substituting x with the given options finds the value that makes both sides equal. The comments under the video add more. One reply lays out three steps: put the value in for the variable, do the arithmetic on each side in the order of operations, then compare the two sides; if they are the same number, the value is a solution. Another reply answers a question about checking your own answer: yes, substitute it back into the original equation, simplify both sides and make sure they are equal. Its example is 5x − 3 = 4x + 3 with x = 6, where 5(6) − 3 is 27 and 4(6) + 3 is 27, so it checks. These are replies in the comment section, not the lesson’s own text.

Symbolab’s algebra calculator page says the same in a section headed Verifying the Solution: substitute your solution into the original equation and see that it satisfies it. Its example is 5x + 2 = x + 10, which the page solves in four steps to x = 2. It then asks whether 5(2) + 2 equals 2 + 10, finds 12 on both sides, and says x = 2 is correct. The page that sells a Verify button therefore also describes the check you can do by hand.

Our worked example, not a page’s: take 9x + 7 = −7. Subtract 7 from both sides to get 9x = −14, so x = −14/9. To check, put it into the original equation. 9 times −14/9 is −14, and −14 + 7 is −7, which is the right side. Had we slipped and written x = −2, then 9 times −2 plus 7 is −11, not −7, and the check would show it. One more point is ours: the check looks only at the final value, so it tells you whether the answer is right and not which step went wrong. Under the Khan video, a reply to a student who cancelled the 3s in 5x − 3 = 4x + 3 says that −3 and +3 are on different sides of the equals sign, so they do not cancel; the reply adds 3 to both sides first.

For a system of two equations, the Nebraska book says to substitute the x- and y-values into each equation and simplify to see whether you get a true statement in both. Its Example 3.1 tests the pair (1, 0) in x − y = 1 and −2x + 3y = 5. The first gives 1 = 1, the second gives −2 = 5, so (1, 0) satisfies the first equation but not the second and is not a solution. Our worked example: for x + y = 5 and x − y = 1, the pair (3, 2) gives 5 and 1, so both are true. The pair (4, 1) gives 5 for the first, which is true, and 3 for the second, which is not 1, so it fails.

The book also carries a caution about solving by substitution: you must substitute one equation into the other, and substituting back into the equation you started with gives a misleading result. That caution is about the solving step, where an answer is being built; the check goes the other way and uses the original equations. The two pieces of advice apply to different jobs and do not conflict.

Symbolab also has a Testing Solutions Calculator page, which describes checking whether points satisfy given equations and inequalities step by step, with examples such as a point against y = 44x. For inequalities the pages we read give no check of their own. Our worked example: −2x > 6 gives x < −3, because dividing by a negative number turns the sign around. Test x = −4: −2 times −4 is 8, and 8 > 6 is true. Test x = 0: 0 > 6 is false. Trying one value from each side of the boundary is the same substitution the pages describe.

A graph estimates; substitution confirms

The Nebraska book uses graphs for systems, and it is clear about what they do. It says to use the graph to estimate the point where the lines intersect and then check whether that point solves the original system. In its first graphed example the intersection appears to be (−1, 3), and in a second it appears to be (3, −4); each is followed by a check. The graph supplies the estimate and the substitution supplies the confirmation.

A Desmos graph titled Solving Equations shows the same order for one equation. It writes 5x + 2 = −1 as two lines, y = 5x + 2 and y = −1, tells you to click the point where they cross, and reports (−0.6, −1), so x is −0.6. A last line then works out 5(−0.6) + 2 and gets −1. That is a graph hosted on desmos.com, one example, not a page of the Desmos user guide.

The Desmos Graphing Calculator guide says the calculator can graph functions, plot tables of data and evaluate expressions, and that its expression list lets you plot points, graph equations and evaluate expressions. The guide text we read does not describe checking a solution, so we do not claim a Desmos method beyond the example above. One arithmetic note of ours: a graph shows x as a decimal, so for 9x + 7 = −7 you would compare the crossing point with −14/9, which is about −1.56, rather than expect to see the fraction.

What the tool pages say about steps and checking

Symbolab. The algebra calculator page has a box labelled Type your Answer with a Verify button, and the line beside it reads Subscribe to verify your answer. The menu has an entry called Verify Solution. The pages we read do not say what Verify checks or what the subscription costs. Symbolab’s home page reached us in Italian, with the entry as Verifica soluzione; the calculator pages were in English.

Mathway. The page says Mathway is free to use, that you can get step-by-step solutions without signing up, and that an optional subscription unlocks the full work shown for every step. You type the problem or upload a photo. The page calls Mathway AI-powered and says it is backed by Chegg; its footer has links named Academic Integrity and Honor Code, which we did not open.

Wolfram|Alpha Pro. The Pro page says step-by-step buttons expand answers and explain how the answer was found. It lists Show Intermediate Steps, Choose a Method, which it describes as using your classroom’s teaching method, and Show Hints, which it says are meant to guide you towards finding the solution yourself. The page shows a monthly price, but currency and amount depend on where it is read, so we leave it out. The examples page says the step-by-step solutions cover over 200 topics, and one of its linear examples is solve 2x + 3 = 6.

Photomath. The home page describes scanning a problem and getting a solution, sometimes with several methods, and asks you to check each step to make sure you understand the solution. That is a check of understanding. QuickMath. The page title calls it a step-by-step math problem solver, and the text lists solving equations, inequalities and systems, simplifying, factoring, expanding and graphing.

The Mathway, Photomath, Wolfram|Alpha and QuickMath pages we read do not describe using the tool to check an answer you worked by hand. They differ on what is behind a subscription: Symbolab asks for one for Verify, Mathway for the full work of every step, and Wolfram|Alpha for its Pro steps. We read no page that compares the tools with each other, so this page ranks none.

Where the tools can be wrong

Symbolab is the one tool page we read that says so. Its algebra page states that AI explanations are generated using OpenAI technology and that AI-generated content may present inaccurate or offensive content that does not represent Symbolab’s view, and a second line beside its chat box says AI may present inaccurate content. Mathway calls itself AI-powered, and the page we read does not mention errors. The Photomath, QuickMath and Wolfram|Alpha pages we read do not mention errors either.

The Wolfram|Alpha blog gives a different kind of limit, and an old one. In a post of 15 January 2014 it says Pro users get unlimited access to step-by-step solutions. In April 2014 a reader asked how to force the step-by-step button when it was missing, and the team replied that it was continually working to add new step-by-step results and asked for feedback on any missing one. Read as a 2014 exchange, it says a problem could come without steps. The current pages we read do not address it.

The measurement of errors we read is a 2025 study in the Proceedings of the National Academy of Sciences by Bastani and colleagues, run at a high school in Turkey. Its abstract says generative AI is fallible and users must check its outputs. The authors asked their GPT Base assistant, a chat tool based on GPT-4, “What is the answer?” ten times for each of 57 practice problems. It gave a correct answer 51% of the time on average, with logical errors 42% of the time and arithmetic errors 8% of the time. Those figures describe that assistant. They do not describe Symbolab, Mathway, Photomath or Wolfram|Alpha, and we do not apply them to any of them. The same study found that students with GPT Base scored 17% lower on the exam without the tool than the control group; our math solver page covers it.

Our reading, not a finding: when a tool’s answer and yours disagree, neither has yet been shown right. Putting each into the original equation settles it without trusting either one.

A routine, and what the pages do not say

The pages we read do not give one sequence for checking your own work. This order is ours, assembled from them:

1. Work the problem by hand and write the final value or pair.
2. Substitute it into the original equation, or into each original equation for a system, and simplify both sides (Khan Academy, Symbolab, Nebraska).
3. If a graph helps, treat its crossing point as an estimate and substitute it too (Nebraska, Desmos).
4. Only then compare with a tool, and read each step it shows, which is what the Photomath page asks; the Wolfram|Alpha Pro page says its hints are meant to guide you towards finding the solution yourself.
5. If the tool disagrees, put both answers into the original equation. Symbolab warns that its AI explanations may be inaccurate, so the substitution is the tie-breaker.

Some things the pages we read do not say. The Mathway, Photomath, Wolfram|Alpha and QuickMath pages do not say how often their solvers are wrong. The Symbolab pages do not say what Verify checks. The Desmos guide text does not describe checking solutions. We read nothing about Microsoft Math Solver, so we write nothing about it. The other AI solving and paid-help sites were not opened, so nothing is written about them.