Free Algebra Solver

Accuracy and limitations

What the solver can verify today

Accuracy starts with a narrow, testable claim. This page distinguishes supported problem families from unsupported ones and explains the evidence behind each verification state.
Applies to the current PHP solver Last reviewed

What “accurate” means on this website

A result is considered accurate only within the documented input syntax, number domain, and problem family. The solver should identify the correct class, apply valid transformations, return the complete supported answer, and provide appropriate verification evidence. A visually polished answer without those conditions is not enough.

No claim of universal or perfect mathematical accuracy is made. Software defects, ambiguous input, browser problems, hosting failures, and untested edge cases can occur. Important academic or professional work should be checked independently.

Supported problem families

Current solver coverage
Problem familyCurrent support
Linear equations in xInteger, decimal, and fractional coefficients; variable terms may appear on both sides; one, none, or infinitely many solutions.
Quadratic equations in xStandard-form classification, discriminant analysis, rational factoring where available, exact radicals, and real or complex roots.
Linear inequalities in xFirst-degree inequalities with explicit reversal when multiplying or dividing by a negative value.
Linear absolute-value equationsAn isolated supported absolute-value expression with positive, zero, or negative target analysis and complete case checking.
Polynomial expressionsSimplification and expansion through the supported parser range, combining matching powers, and rational factorization for recognized cases.
Exact fraction arithmeticNumeric expressions and direct addition, subtraction, multiplication, or division of fractions with reduction and visual models.
Least common multiples and greatest common divisorsTwo to eight positive integers with prime factorizations, maximum and minimum shared exponents, and exact divisibility checks.
Ratio simplificationTwo to six nonnegative whole-number, fraction, or decimal parts reduced to an exact whole-number ratio.
Polynomial evaluationExact substitution of an integer, decimal, or fraction for x in a supported polynomial through degree four.
Polynomial graphingConstant through quartic functions of x with exact coefficients, sampled rendering, adjustable windows, and selected linear or quadratic features.

How to interpret a verification label

“Verified” means the engine produced candidate-level or equivalence evidence and used the relevant problem classification to establish completeness within the supported domain. It does not mean a human teacher reviewed that individual submission.

“Equivalent” is used for simplification, factoring, or expansion when exact polynomial comparison confirms matching coefficients. “Exact” identifies rational arithmetic or substitution completed without floating-point rounding. “Function checked” means the graph is rendered from exact normalized coefficients, while the visible curve itself remains a sampled display. “Review needed” means complete independent evidence was unavailable.

Problems outside the current release

The site does not currently claim support for simultaneous systems, matrices, logarithmic or exponential equations, trigonometric equations, calculus, general radical equations, equations with the variable in a denominator, or arbitrary higher-degree polynomial solving. Compound, rational, and absolute-value inequalities may also require methods outside the current linear inequality workflow.

An unsupported message is a capability boundary, not a statement that the problem has no solution. Use a method-specific educational resource or qualified instructor for those problem types.

Input interpretation and user checks

Parentheses, fraction bars, exponent notation, and relation symbols affect meaning. Review the “Interpreted as” line before relying on a result. For example, 1/2x may be read differently from 1/(2x), so grouping is essential when the intended structure could be ambiguous.

After solving, compare the normalized problem with the original source and inspect the first step. Substitution is useful only when it checks the problem you meant to enter.

Reporting a suspected error

A useful report includes the exact input, selected operation, number domain, displayed answer, the first step believed to be wrong, expected result, device, and browser. Do not include a student name, school record, login credential, or other personal information.

Confirmed correctness defects should receive priority over cosmetic issues, and material corrections should be described in the public changelog when appropriate. The current contact limitation is explained on the Contact page.