Solve an inequality to see its solution shaded on the number line.
Solve an inequality to see f(x) graphed with the solution region shaded.
Template:
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Sign chartfind critical points → test intervals → pick those that satisfyAbsolute value|f| < a ⇒ -a < f < a, |f| > a ⇒ f > a or f < -aRationalinclude numerator zeros, exclude denominator zeros (open circles)
This solver handles linear (2x + 3 > 7), quadratic (x² − 4 ≥ 0), polynomial (x³ − x < 0), rational ((x − 1)/(x + 2) > 0), absolute value (|x − 3| < 5), and compound (1 < 2x + 3 < 7) inequalities. It finds all solutions using the sign chart method and presents results in interval notation and set-builder notation.
The sign chart method works by: (1) moving all terms to one side to get f(x) > 0, (2) finding critical points where f(x) = 0 or is undefined, (3) testing the sign of f(x) in each interval between critical points, (4) selecting intervals where the sign satisfies the inequality. Works for all polynomial and rational inequalities.
Interval notation uses parentheses ( ) for excluded endpoints (strict inequalities) and brackets [ ] for included endpoints (non-strict). For example, (−2, 3] means all numbers greater than −2 and up to 3. Union symbol ∪ combines disjoint intervals: (−∞, −2) ∪ (2, ∞). The empty set is shown as ∅ and all real numbers as (−∞, ∞).
The less-than symbol (<) is a strict inequality excluding the endpoint — shown with open circles on the number line and parentheses in interval notation. The less-than-or-equal symbol (≤) is non-strict and includes the endpoint — shown with closed/filled circles and brackets. For example, x < 2 gives (−∞, 2) while x ≤ 2 gives (−∞, 2].
Yes. After solving an inequality you can: (1) Download as PDF with the original inequality, solution, sign chart, and steps; (2) Copy as LaTeX for papers and documents; (3) Copy as plain text; or (4) Generate a shareable URL. The PDF includes a watermark and date.
Yes — completely free with no signup, no account, and no limits. All computation runs client-side in your browser using the sign chart method. You get step-by-step solutions, interactive number line, function graph, PDF download, LaTeX export, and a Python SymPy compiler.
Yes. Click the 📷 Scan button and upload (or drop in) a photo of a handwritten or printed inequality. The AI vision model extracts the inequality (preserving < ≤ > ≥ symbols and absolute-value bars), fills the math field automatically, and detects the inequality type. Works on phone snapshots, textbook pages, whiteboard photos, and worksheet scans.
Covers Algebra 1 (linear inequalities, compound), Algebra 2 (quadratic, polynomial, rational, absolute value), Precalculus (sign chart analysis), and college algebra. Aligned with Common Core HSA-REI.B.3 and HSA-CED.A.1, plus CBSE/ICSE class 9–11 inequalities chapters. SAT, ACT, and JEE Mains practice covered.
Click the Practice Worksheet — 1,500+ inequalities with answer key button below the result. The worksheet engine generates printable problem sets across 4 difficulty tiers (basic, medium, hard, scholar) and 35 problem types — linear (with parens, fractions, sign-flip), quadratic (factored and general), polynomial (cubic), rational, absolute-value (simple, complex, compound), log, exponential, system of linear inequalities, NCERT Class 11 word problems (IQ/mental-age, acid-mixing, rectangle perimeter, score threshold), and IIT-JEE Advanced / Putnam scholar problems (exp-quadratic substitution, log fractional base, nested logs, square-root inequalities, modulus-vs-modulus, AM-GM optimisation, Cauchy-Schwarz, Bernoulli's inequality). Every problem and answer is CAS-verified.