Free AI Algebra Solver

Algebra forms the foundation of every math course you will take from middle school through college. Our free AI algebra solver handles everything from basic one-step equations to complex systems with multiple variables. Upload a photo or type your equation and get a complete step-by-step solution in seconds.

Linear Equations and Inequalities

The solver handles one-variable and multi-variable linear equations, showing each isolation step clearly. It demonstrates proper handling of negative signs, fractions, and decimal coefficients. For inequalities, the solver correctly flips the inequality sign when multiplying or dividing by a negative number and expresses solutions in interval notation.

Systems of linear equations are solved using substitution, elimination, and matrix methods. The AI selects the most efficient approach based on the structure of the system and explains why that method was chosen. Systems with two, three, or more variables are all supported.

Quadratic Equations

Quadratic equations appear constantly in Algebra I, Algebra II, and standardized tests like the SAT. The solver demonstrates factoring, completing the square, and the quadratic formula. It identifies the discriminant, determines the number and type of solutions (real or complex), and graphs the parabola's key features including vertex, axis of symmetry, and intercepts.

When a quadratic can be factored, the solver shows the factoring process first as it is the preferred method on most tests. When factoring is not practical, it seamlessly switches to the quadratic formula with clear substitution steps.

Polynomial Operations and Factoring

The AI handles polynomial addition, subtraction, multiplication, and long division. For factoring, it applies greatest common factor extraction, grouping, difference of squares, sum and difference of cubes, and general trinomial factoring. Each technique is labeled so you know which method applies to different polynomial structures.

Rational Expressions

Simplifying, multiplying, dividing, adding, and subtracting rational expressions requires careful factoring and attention to domain restrictions. The solver identifies excluded values, finds common denominators, and simplifies completely. It also solves rational equations and checks for extraneous solutions.

Exponents and Logarithms

Exponential and logarithmic equations are solved with clear application of logarithmic properties including the product rule, quotient rule, power rule, and change of base formula. The solver handles natural logarithms, common logarithms, and logarithms with arbitrary bases. Exponential growth and decay word problems are also supported.

Functions and Graphing

The solver analyzes functions for domain, range, intercepts, symmetry, and transformations. It composes and decomposes functions, finds inverses, and identifies parent functions. It also handles piecewise functions, step functions, and greatest integer functions. This covers the function analysis skills tested in Algebra II and pre-calculus courses across the United States.

Inequalities and Absolute Value Inequalities

The solver handles linear inequalities, compound inequalities, and quadratic inequalities with proper solution set notation. It correctly represents solutions on number lines and in interval notation, identifies open versus closed boundaries, and handles the special cases that arise when multiplying or dividing both sides by a negative number. Absolute value inequalities are decomposed into compound inequality form and solved systematically, which is a technique that appears on virtually every SAT math exam.

Absolute Value and Piecewise Functions

Absolute value equations and inequalities require careful handling because they split into multiple cases. The solver demonstrates how to isolate the absolute value expression, create the positive and negative case equations, solve each case independently, and check solutions against the original constraint. It also handles piecewise-defined functions by evaluating each piece over its defined interval and graphing the result. These topics appear frequently on the SAT and in Algebra II courses.

Matrices and Determinants

Matrix operations including addition, scalar multiplication, matrix multiplication, finding determinants, and computing inverse matrices are handled with clear step-by-step notation. The solver applies Cramer's rule and row reduction to solve systems of equations in matrix form. These skills bridge algebra with linear algebra and are tested in many pre-calculus and college algebra courses.

Sequences and Series in Algebra

Arithmetic and geometric sequences and series are fundamental algebra topics. The solver identifies the common difference or common ratio, generates explicit and recursive formulas, computes specific terms, and evaluates finite and infinite sums. It applies the formulas for arithmetic series sums and geometric series sums with clear substitution steps. Understanding sequences in algebra provides essential preparation for the more advanced series work encountered in calculus.

Complex Numbers

Operations with complex numbers including addition, subtraction, multiplication, division, and computing powers using De Moivre's theorem are solved with detailed real and imaginary part tracking. The solver plots complex numbers on the complex plane and converts between rectangular and polar form. These skills are tested in Algebra II and pre-calculus courses and provide groundwork for engineering and physics applications. The solver also factors polynomials over the complex numbers, finding all roots including complex conjugate pairs, which is essential for understanding the Fundamental Theorem of Algebra stating that every polynomial of degree n has exactly n roots when counted with multiplicity in the complex number system.

Why Algebra Matters

Every higher math course assumes algebra fluency. Struggling with algebra makes calculus, statistics, and geometry significantly harder. Use our AI solver to identify and fill gaps in your algebra knowledge before they compound into bigger problems. Whether you are preparing for the SAT, working through word problems, or building toward AP Calculus, strong algebra skills are the foundation of your success. Check out our comparison of AI math solvers to see how our free tool stacks up against paid alternatives.