Case analysis.
Split absolute value into the two cases (negative and non-negative).
Setup
AI Solver by AskSia
Modulus Inequality Solver: solved by case analysis
Type or photograph the inequality (e.g., |x minus 3| less than 5, or |2x plus 1| greater than 4). AskSia splits into cases, solves each, combines the solution sets, and writes the answer in interval notation.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
How do you solve modulus (absolute value) inequalities?
A modulus inequality involves an absolute value expression compared to a number. The standard approach: rewrite the inequality without absolute values using the definition. For |expression| less than k (with k positive), rewrite as minus k less than expression less than k. For |expression| greater than k, rewrite as expression less than minus k or expression greater than k. Solve each resulting inequality and combine using AND (less than) or OR (greater than). Write the final solution in interval notation.
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solution accuracy
50M+
problems solved
~1.5s
avg solve time
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study-ready explanations
Why AskSia Solver
Why students use AskSia for Modulus Inequality.
Every step transparent, every answer self-checked.
Solve each case.
Each linear or quadratic inequality solved separately.
Solve
Combine sets.
AND or OR based on the original inequality direction.
Combine
Interval notation output.
Final answer in standard interval notation.
Output
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Modulus Inequality problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
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Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
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Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Modulus Inequality solver covers.
Linear inside.
|x minus a| less than k. Standard case.
Linear
Linear with greater than.
|x minus a| greater than k. Splits into two disjoint cases.
Greater than
Quadratic inside.
|x squared minus k| less than m. Solve the resulting compound inequality.
Quadratic
Compound inequalities.
Multiple absolute values, broken into cases by sign combinations.
Compound
Word problems.
Distance, error tolerance, often modeled by absolute value inequalities.
Word problem
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
How does |x| less than k translate?
|x| less than k (where k is a positive real number) means x is within distance k of zero, which is equivalent to minus k less than x less than k. So |x minus 3| less than 5 becomes minus 5 less than (x minus 3) less than 5, which gives minus 2 less than x less than 8. The solution is the open interval from minus 2 to 8.
How does |x| greater than k translate?
|x| greater than k (where k is positive) means x is more than distance k from zero, which is equivalent to x less than minus k or x greater than k. So |x minus 3| greater than 5 becomes x minus 3 less than minus 5 or x minus 3 greater than 5, giving x less than minus 2 or x greater than 8. The solution is the union of two open intervals.
What if k is negative?
|expression| less than k with k negative has no solution: an absolute value is never negative, so it cannot be less than a negative number. |expression| greater than k with k negative is always true: the absolute value is always at least zero, which is greater than any negative number. AskSia recognizes these edge cases and reports accordingly.
How are quadratic absolute values handled?
For |quadratic| less than k, set up the case minus k less than quadratic less than k. This is a compound inequality that requires solving two related quadratic inequalities. AskSia factors and uses sign analysis on each. The final solution can be a union or intersection of intervals depending on the case. AskSia presents the complete answer in interval notation.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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Cases, solve, combine, interval.
Join 2M+ students using AskSia to solve modulus inequality problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.
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