FAQ
Frequently asked questions
What types of inequalities does this calculator solve?
The calculator solves linear, quadratic, absolute-value, rational, compound, and one-variable system inequalities, plus linear two-variable inequalities for coordinate-plane graphing. It explains the algebra and shows the matching graph.
Does the inequality calculator show steps?
Yes. Every supported inequality includes step-by-step reasoning so students can see how the expression is rearranged, where critical points come from, and why each interval is included or excluded.
Can I use the calculator for interval notation?
Yes. Every solution includes interval notation and set notation. If the answer is all real numbers or no solution, the calculator states that clearly.
When does the inequality sign flip?
The sign flips only when you multiply or divide both sides by a negative number. The calculator highlights that rule in the step list when it applies.
Does the calculator support graphing inequalities?
Yes. One-variable inequalities appear on an animated number line, and linear two-variable inequalities appear on a coordinate plane with a shaded half-plane and solid or dashed boundary line.
Is this inequality calculator free?
Yes. The core calculator, steps, graph, and notation outputs are free to use on desktop and mobile.
Can the calculator solve quadratic inequalities with two roots?
Yes. When a quadratic has two real roots, the calculator identifies the critical points, tests the intervals they create, and shows the final answer in both notation and graph form.
Can I share a solved inequality with someone else?
Yes. The current problem can be stored in the URL query string, so you can copy the link or the iframe embed code and send the exact same setup to students, teammates, or readers.
Can the calculator solve rational inequalities?
Yes. The current release supports rational inequalities that can be analyzed with a sign chart, such as (x + 1) / (x - 2) > 0.
Can I solve a system of inequalities?
Yes. Separate each inequality with a semicolon, a new line, or the word and. One-variable systems are intersected on the number line, and linear two-variable systems are graphed as a shared feasible region.
Does the calculator work for two variables?
Yes. Enter a linear inequality such as 2x + 3y < 6 or y >= -x + 4 and the calculator will graph the correct half-plane on a coordinate grid. It also supports linear two-variable systems entered with semicolons.
Can I test whether a point satisfies a two-variable inequality?
Yes. When the result is graphed on the coordinate plane, the point checker lets you enter an x-value and y-value to verify whether that coordinate lies in the shaded region.
What is the difference between open and closed endpoints?
Open endpoints are used for strict inequalities like < and >, while closed endpoints are used for inclusive inequalities like <= and >=.
Why is the boundary line dashed for some graphs?
A dashed boundary means points on the line are not part of the solution set because the inequality is strict. A solid boundary means the line itself is included.
Can the calculator handle absolute value inequalities with steps?
Yes. Absolute value inequalities include case-splitting steps so you can see why the answer becomes either an overlap or an outside union.
Do I need to click a solve button?
No. The calculator updates in real time as you type, so the steps, notation, and graph refresh automatically.
Can I use LaTeX-style input?
Basic math-friendly input is supported, including symbols such as \le, \ge, powers, multiplication marks, and absolute-value bars.
Does the calculator keep my history?
Yes. The latest calculations are stored locally in your browser so you can reload recent problems without creating an account.
Does the calculator have a practice mode?
Yes. Practice mode can generate fresh linear, quadratic, absolute-value, rational, system, compound, and graphing prompts so learners can solve first and then compare with the official answer.
What is focus mode?
Focus mode opens the calculator in a full-screen overlay that removes the surrounding page sections so you can work through a problem with fewer distractions.
Can the calculator read the steps aloud?
Yes on supported browsers. The steps panel includes a built-in audio reader powered by the Web Speech API, so you can play, pause, resume, or stop the walkthrough.
Can I export the graph image?
Yes. Both number-line graphs and coordinate-plane graphs can be downloaded as SVG or PNG directly from the browser.
Can I export my saved history to PDF?
Yes. The history panel can open a print-ready export view so you can save the latest calculations as a PDF from the browser's print dialog.
Does the site support dark mode?
Yes. The theme can follow your system setting or be switched manually, and the choice is stored locally on your device.
Can teachers embed this calculator in a lesson page?
Yes. The share panel generates an iframe snippet so the calculator can be embedded in static lesson pages, blogs, or classroom resources.
What happens when I multiply an inequality by a negative number?
The inequality symbol flips direction. The calculator calls out that rule explicitly in the step list whenever it applies.
Does the calculator work on mobile?
Yes. The interface is mobile-first, with a tap-friendly math keyboard, responsive graphs, and copyable share links that work on phones and tablets.
Can I use this calculator for homework checking?
Yes. It is useful for checking answers and understanding the method, but you should still review each step so you know why the solution works.
How do you solve a linear inequality?
Move like terms together, isolate the variable, and flip the inequality only if you multiply or divide by a negative number.
Can linear inequalities have compound answers?
Yes. Chained inequalities and some absolute-value transformations lead to bounded intervals such as 1 < x <= 3.
Why do quadratic inequalities use intervals?
A quadratic can change sign only at its real roots, so the real number line splits into intervals that can each be tested once.
What if a quadratic has no real roots?
Then the quadratic keeps the same sign for every real x. The answer is either all real numbers or no real solution.
What does an absolute value inequality mean?
It measures distance from zero. For example, |x - 2| <= 4 means x is within 4 units of 2.
When do absolute value inequalities use AND or OR?
|A| <= k gives an AND interval, while |A| >= k gives an OR answer with two outer intervals.
How do you solve a chained inequality?
Treat the middle expression as shared, split the chain into two inequalities, solve each one, and intersect the valid values.
Do chained inequalities keep the same direction?
Yes, unless a step multiplies or divides a side by a negative number. Then that comparison flips.
Why are some x-values excluded in rational inequalities?
Any value that makes a denominator equal zero is excluded from the domain and cannot appear in the final answer.
Should I multiply both sides by the denominator to solve a rational inequality?
Not blindly. The sign of the denominator can change across intervals, so sign-chart analysis is safer than cross-multiplying without restrictions.
What does an open circle mean on an inequality graph?
It means the endpoint is not included in the solution, which happens with < or >.
Why are some boundary lines dashed on the coordinate plane?
A dashed line means the boundary itself is excluded because the inequality is strict. Inclusive inequalities use a solid boundary.
When do I use a bracket instead of a parenthesis?
Use a bracket when an endpoint is included and a parenthesis when it is excluded.
Can this page convert interval notation back into an inequality?
Yes. The interval notation page supports both directions, so you can start with an interval such as (3, +∞) and convert it back to x > 3.
What is the solution to a system of inequalities?
It is the feasible region: the set of all points that satisfy every inequality in the system at the same time.
How do you find the corner points of a feasible region?
Write the boundary equation for each constraint, solve the boundary pairs, and keep only the intersection points that satisfy the full system.