{
  "title": "Inequality solution grapher",
  "human_url": "https://happytails.ai/en/calculators/inequality-solution-grapher/",
  "agent_url": "https://happytails.ai/agents/en/calculators/inequality-solution-grapher/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/inequality-solution-grapher.md",
  "content": "Inequality solution grapher\nSolve a polynomial, rational or abs inequality exactly with a sign chart and see the solution on a number line. Endpoints are marked open, closed or excluded.\nHow to use Inequality solution grapher\nType the inequality, such as (x - 1)/(x + 2) <= 3 or 1 < 2x + 3 <= 7.\nRun the solver to find every zero and excluded value.\nRead the sign chart and the solution in interval notation.\nDownload the JSON report, the CSV sign chart or the number line SVG.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nUseful next steps\nGraphing calculator\nQuadratic formula calculator\nLinear system solver\nInequalities are limited to 1,000 characters, one variable, 24 nesting levels, 100 digits per number, 4 abs terms and polynomial factors up to degree 24. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report, a CSV sign chart and an SVG number line.\nHow it solves\nEverything is moved to one side. The zeros of the numerators, the excluded values of the denominators and the points where an abs term changes sign split the number line. Each piece is tested at an exact sample point, so the signs are proven, not estimated. Method: OpenStax, College Algebra 2e, section 2.7 Linear Inequalities and Absolute Value Inequalities (2021); Basu, Pollack and Roy, Algorithms in Real Algebraic Geometry, chapter 2 (2006).\nIrrational endpoints\nEndpoints such as 1 + sqrt(2) are written exactly. Roots of cubic or higher factors are named r1, r2 and so on, with their polynomial, an isolating interval and a decimal value.\nWhat you can enter\nUse <, <=, >, >=, = or != once, or twice for a double inequality. Square roots, logarithms, trigonometric functions, pi and e are not supported. The number line places points in order and is not drawn to scale.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "name": "Graphing calculator",
      "url": "https://happytails.ai/en/calculators/graphing-calculator/"
    },
    {
      "name": "Quadratic formula calculator",
      "url": "https://happytails.ai/en/calculators/quadratic-formula/"
    },
    {
      "name": "Linear system solver",
      "url": "https://happytails.ai/en/calculators/linear-system-solver/"
    }
  ],
  "tool": {
    "id": "inequality-solution-grapher",
    "category": "calculators",
    "built": true,
    "requirements": "Inequalities are limited to 1,000 characters, one variable, 24 nesting levels, 100 digits per number, 4 abs terms and polynomial factors up to degree 24. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report, a CSV sign chart and an SVG number line.",
    "implementation": {
      "fields": [],
      "presentation": "metrics",
      "inputCodeDirection": "ltr",
      "registrationFamily": "exact-math-functions",
      "inputMaxLength": 1000,
      "inputErrorCode": "EXACT_MATH_FUNCTIONS_EXPRESSION_TOO_LONG",
      "note": "Solves polynomial, rational and abs inequalities exactly on your device with a sign chart, for inputs up to 1,000 characters.",
      "experience": {
        "automatic": false,
        "single": true,
        "inputMaxLength": 1000,
        "inputMode": "text",
        "label": "Inequality",
        "placeholder": "(x - 1)/(x + 2) <= 3",
        "help": "Use one variable and <, <=, >, >=, = or !=, such as x^2 - 4 < 0. Up to 1,000 characters. Review the settings before running.",
        "helpParts": [
          "Use one variable and <, <=, >, >=, = or !=, such as x^2 - 4 < 0.",
          "Up to 1,000 characters.",
          "Review the settings before running."
        ],
        "action": null
      },
      "mode": "explicit",
      "interactive": false
    },
    "execution": "Browser interface",
    "api": null,
    "browser_agent": {
      "supported": true,
      "name": "run_current_tool",
      "discovery": "WebMCP on the human page in a supporting browser",
      "verification": "See audit/API-AUDIT.md; availability is not verification"
    }
  },
  "markdown": "# Inequality solution grapher\n\n- Human page: https://happytails.ai/en/calculators/inequality-solution-grapher/\n- Markdown: https://happytails.ai/en/calculators/inequality-solution-grapher.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/inequality-solution-grapher/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `inequality-solution-grapher` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Use the visible action or interactive controls. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nSolves polynomial, rational and abs inequalities exactly on your device with a sign chart, for inputs up to 1,000 characters.\n\n### Inputs and settings\n\nText input: Inequality.\n\nExample or placeholder shown in the interface (not a validated fixture):\n\n```text\n(x - 1)/(x + 2) <= 3\n```\n\nUse one variable and <, <=, >, >=, = or !=, such as x^2 - 4 < 0. Up to 1,000 characters. Review the settings before running.\n\nNo additional settings are declared for this tool.\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nInequalities are limited to 1,000 characters, one variable, 24 nesting levels, 100 digits per number, 4 abs terms and polynomial factors up to degree 24. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report, a CSV sign chart and an SVG number line.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"inequality-solution-grapher\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"Inequalities are limited to 1,000 characters, one variable, 24 nesting levels, 100 digits per number, 4 abs terms and polynomial factors up to degree 24. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report, a CSV sign chart and an SVG number line.\",\n  \"implementation\": {\n    \"fields\": [],\n    \"presentation\": \"metrics\",\n    \"inputCodeDirection\": \"ltr\",\n    \"registrationFamily\": \"exact-math-functions\",\n    \"inputMaxLength\": 1000,\n    \"inputErrorCode\": \"EXACT_MATH_FUNCTIONS_EXPRESSION_TOO_LONG\",\n    \"note\": \"Solves polynomial, rational and abs inequalities exactly on your device with a sign chart, for inputs up to 1,000 characters.\",\n    \"experience\": {\n      \"automatic\": false,\n      \"single\": true,\n      \"inputMaxLength\": 1000,\n      \"inputMode\": \"text\",\n      \"label\": \"Inequality\",\n      \"placeholder\": \"(x - 1)/(x + 2) <= 3\",\n      \"help\": \"Use one variable and <, <=, >, >=, = or !=, such as x^2 - 4 < 0. Up to 1,000 characters. Review the settings before running.\",\n      \"helpParts\": [\n        \"Use one variable and <, <=, >, >=, = or !=, such as x^2 - 4 < 0.\",\n        \"Up to 1,000 characters.\",\n        \"Review the settings before running.\"\n      ],\n      \"action\": null\n    },\n    \"mode\": \"explicit\",\n    \"interactive\": false\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": true,\n    \"name\": \"run_current_tool\",\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nSolve a polynomial, rational or abs inequality exactly with a sign chart and see the solution on a number line. Endpoints are marked open, closed or excluded.\n\n### How to use Inequality solution grapher\n\n1. Type the inequality, such as (x - 1)/(x + 2) <= 3 or 1 < 2x + 3 <= 7.\n2. Run the solver to find every zero and excluded value.\n3. Read the sign chart and the solution in interval notation.\n4. Download the JSON report, the CSV sign chart or the number line SVG.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n## Useful next steps\n\n- [Graphing calculator](https://happytails.ai/en/calculators/graphing-calculator/) ([Markdown](https://happytails.ai/en/calculators/graphing-calculator.md))\n\n- [Quadratic formula calculator](https://happytails.ai/en/calculators/quadratic-formula/) ([Markdown](https://happytails.ai/en/calculators/quadratic-formula.md))\n\n- [Linear system solver](https://happytails.ai/en/calculators/linear-system-solver/) ([Markdown](https://happytails.ai/en/calculators/linear-system-solver.md))\n\nInequalities are limited to 1,000 characters, one variable, 24 nesting levels, 100 digits per number, 4 abs terms and polynomial factors up to degree 24. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report, a CSV sign chart and an SVG number line.\n\n## How it solves\n\nEverything is moved to one side. The zeros of the numerators, the excluded values of the denominators and the points where an abs term changes sign split the number line. Each piece is tested at an exact sample point, so the signs are proven, not estimated. Method: OpenStax, College Algebra 2e, section 2.7 Linear Inequalities and Absolute Value Inequalities (2021); Basu, Pollack and Roy, Algorithms in Real Algebraic Geometry, chapter 2 (2006).\n\n### Irrational endpoints\n\nEndpoints such as 1 + sqrt(2) are written exactly. Roots of cubic or higher factors are named r1, r2 and so on, with their polynomial, an isolating interval and a decimal value.\n\n### What you can enter\n\nUse <, <=, >, >=, = or != once, or twice for a double inequality. Square roots, logarithms, trigonometric functions, pi and e are not supported. The number line places points in order and is not drawn to scale.\n"
}