happytails.ai

Inequality solution grapher

Open Inequality solution grapher on Happytails.ai. This view has the same page content and links, with explicit tool capabilities. Read the processing notes before using a tool.

Tool capabilities

{
  "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"
  }
}

Page guide

Solve 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.

How to use Inequality solution grapher
  1. Type the inequality, such as (x - 1)/(x + 2) <= 3 or 1 < 2x + 3 <= 7.
  2. Run the solver to find every zero and excluded value.
  3. Read the sign chart and the solution in interval notation.
  4. Download the JSON report, the CSV sign chart or the number line SVG.

Useful next steps

Graphing calculatorQuadratic formula calculatorLinear system solver

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.

How it solves

Everything 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).

Irrational endpoints

Endpoints 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.

What you can enter

Use <, <=, >, >=, = 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.