Substitute the value.
Put a proposed solution into the original equation with its original brackets and signs. Both sides should evaluate to the same result. This tests whether the value satisfies the task you were given.
Math homework helper
Math that makes sense from the first move.
Choose the route your math question needs: an equation, a theorem or a model from words. Compare the methods and follow detailed guides with checked examples and fresh practice.
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Find your exact sticking point
Math help,
one topic at a time.
Jump straight to the explanation you need.
11 topic routes. Choose an explanation below.
Math
Equations with x on both sides
Collect the variable terms, preserve equality and substitute to check.
MathBrackets and negative signs
Distribute to every term or divide first when the structure allows it.
MathEquations with fractions
Clear denominators while changing every term on both sides.
MathStraight-line graphs
Connect slope, intercept and a simple system of equations.
MathRight triangles and Pythagoras
Identify the hypotenuse before finding a missing side.
MathAngles in triangles
Use marked facts and the appropriate angle relationship.
MathSimilarity and scale factors
Match corresponding sides and distinguish length from area scaling.
MathArea versus perimeter
Choose the requested quantity and the correct dimensional unit.
MathFixed costs and hourly rates
Define the unknown and separate a one-off charge from a rate.
MathPercentages and discounts
Identify the amount the percentage uses before calculating.
MathRate, time and unit conversions
Make time units agree with the rate, then interpret the result.
No matching topic yet.
Try a broader word, clear the subject filter or browse all subject guides. For a question beyond this collection, bring the complete task and your level to Lirno.
Choose the problem type
Equations. Diagrams.
Stories with numbers.
The method begins with the structure of the question. Find the relevant guide and follow an example before asking for help with your own attempt.
Algebra homework help
Algebra
Solve linear equations, handle brackets and fractions, and check a solution against a graph.
Explore the guide
Geometry homework help
Geometry
Choose the right triangle relationship, match similar sides and distinguish area from perimeter.
Explore the guide
Math word problem help
Word problems
Model fixed fees, rates, percentages and comparisons, then return the answer to the story.
Explore the guideStep-by-step math help
The reason between
the lines matters.
For an equation, each valid transformation preserves the solution. For a geometry calculation, a theorem needs its conditions established. For a word problem, the equation should describe the story and its units. A finished number does not show those decisions on its own.
Ask Lirno to explain why the next move applies. Include the method your teacher requires and the point where your attempt stopped. If the tutor uses a shortcut you have not learned, request the representation your course expects.
Consider “solve x² = 25” versus “find a length whose square is 25 cm².” The algebra equation has x = 5 and x = −5; the geometric length is 5 cm. The calculation looks similar, while the allowable result depends on the task. Preserve that distinction when you choose a method and write the final answer.
Get an explanation at the right pace →Check the result
Three ways to know
what needs attention.
Use a check that reaches back to the original question. Repeating an already incorrect line may reproduce the same mistake.
Inspect the context.
A right triangle hypotenuse is longer than either leg. A fare model should reproduce the stated cost. Use the diagram or story to decide whether a calculation answers the requested quantity.
Explain the operation.
Name the relationship or rule behind each move. If a step is only something you remember copying, ask why it is allowed and practice it in a smaller problem before continuing.
Math from a photo
Keep every
small symbol clear.
A negative sign, exponent or fraction bar can change the problem. Capture the instruction and any diagram along with the equation. If the worksheet has several exercises, tell Lirno which one to discuss first.
Review the captured question before following the explanation. When something seems wrong, check the input as well as the working. A mathematically valid answer can still be the answer to a misread question.
Then add your attempt and a focused request: one hint, an explanation of the transition or a check of the first incorrect line. Keep the parts of your work that are valid and repair the specific decision that needs attention.
For example, −3² means −(3²) = −9, while (−3)² = 9. A faint pair of brackets can reverse the result. If the captured text is ambiguous, clarify the grouping before asking for the calculation. This is an input check, not a reason to repeat the same working more slowly.
Prepare a useful math scan →Match the help to the difficulty
What kind of
math problem is this?
Before asking for an answer, identify whether the difficulty is in the setup, the operation or the interpretation. Those problems need different tutoring questions.
Use a short request that points to the decision. Include any required method and keep the original expression or diagram beside the response.
| Example task | The first decision | Go to the method |
|---|---|---|
| Solve 3(x − 2) = 15 | Divide by 3 first, or distribute 3 to both terms. Both valid routes give x = 7. | Brackets and equation methods → |
| Right triangle: hypotenuse 13, leg 5 | The missing side is a leg. Subtract the squares: b² = 169 − 25 = 144, so b = 12. | Missing-side geometry → |
| $72 after a 20% discount | The original price is the percentage base. Solve 0.80p = 72 to find p = $90. | Reverse-percentage practice → |
| 4x + 2 = 4x + 9 | Subtracting 4x leaves 2 = 9. The false statement means there is no solution. | Equations with no solution → |
A correct calculation can still answer the wrong quantity. Check the setup before repeating the arithmetic.
Move beyond the worked answer
Change one detail.
Keep the reason.
After an example becomes clear, change one number while keeping the structure. Can you choose the method again? Then change the representation: express a fare equation as a table, describe a graph in words or sketch the relationship in a geometry problem.
Explain which parts stayed the same and which parts changed. That comparison helps you distinguish a reusable method from a sequence tied to one set of values. If the method stops applying, identify the condition that changed.
Save a recurring error with its correction, then use a fresh attempt to test the idea. You can use Lirno’s Mistake Book and practice tools to keep that review focused.
Keep the correction that matters →FAQs
Your math questions.
Can Lirno explain math from a picture?
Yes. Use a clear photo of the full problem and check the captured symbols before following the response. Add your attempt and the kind of help you want.
Can I ask for a hint instead of the answer?
Ask for one hint without the final answer. Try the move yourself, then follow up with the part that still feels unclear.
Does this page solve a new equation online?
The website shows prepared examples. Live tutoring for your own equation is in the Lirno app.
Your next math question starts here.
Scan or type your problem in Lirno and work through the step you need.
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