Algebra Calculators

Solve equations involving absolute values step by step. Shows both positive and negative cases with detailed explanations and verification.

Solve inequalities involving absolute values (e.g., |x+a| < b, |x-2| > 3). Understand 'and' vs 'or' conditions with detailed step-by-step solutions.

Solve classic age word problems step by step: one person N years older than another, ratios in Y years, three-person age ratios and father-son puzzles. Sets up the algebra, solves the system, verifies it and draws a timeline.

Simplify complex algebraic expressions by combining like terms, applying the distributive property, and reducing fractions. Features step-by-step solutions, multiple simplification modes, and detailed explanations.

Expand (a+b)^n using the binomial theorem. Get step-by-step expansion with each term, binomial coefficients, Pascal's triangle visualization, and detailed coefficient analysis.

Solve classic coin word problems step by step: N coins totalling a given amount, twice as many quarters as dimes, three-coin mixtures with count relationships, and fewest coins to make an amount. Animates the coin stacks.

Solve quadratic equations by completing the square. Get detailed step-by-step algebraic work, vertex form, geometric visualization, and interactive parabola graph.

Solve any cubic equation ax³+bx²+cx+d=0 using Cardano's formula. Get all three roots (real and complex), step-by-step solution, discriminant analysis, and interactive graph.

Use Descartes' Rule of Signs to determine the possible number of positive and negative real roots of any polynomial. Enter coefficients and see step-by-step sign change analysis with visual diagrams.

Solve for distance, speed or time given the other two. Pick the unknown on an interactive triangle, mix units freely, enter time as 1h 30m or 5400 sec, and use bonus modes for multi-leg average and round-trip harmonic-mean speed.

Determine the domain (possible inputs) and range (possible outputs) of algebraic functions with step-by-step analysis and interval notation.

Multiply and expand polynomials (binomials, trinomials, and higher-degree expressions) using FOIL method and Binomial Theorem. Get step-by-step solutions with detailed explanations.

Solve exponential equations step by step. Supports simple, linear exponent, coefficient, two-base, and quadratic-in-exponential forms. Get detailed solutions with domain analysis and interactive graphs.

Calculate the composition of two functions (f ∘ g)(x) and (g ∘ f)(x) with detailed step-by-step instructions showing how to compose functions algebraically.

Visualize algebraic functions on an interactive coordinate system. Plot multiple equations, identify key features like intercepts, asymptotes, and analyze function behavior.

Determine whether a function is even, odd or neither, with a step-by-step algebraic proof, symmetry graph, numerical verification table and even-odd decomposition. Handles polynomial, trig, exponential, log and absolute value functions.

Solve linear, quadratic, polynomial, and rational inequalities with step-by-step solutions. Display results graphically on a number line and in interval notation.

Calculate the inverse function f^(-1)(x) of a given function f(x) with detailed step-by-step instructions showing how to find the inverse algebraically.

Solve single-variable linear equations (e.g., ax + b = c) with detailed step-by-step solutions. Shows all algebraic manipulations and verifies the answer.

Solve literal equations and rearrange multi-variable formulas. Enter any equation like A = πr², choose a variable, and get the isolated solution with step-by-step algebraic manipulation.

Solve logarithmic equations step by step. Supports log, ln, and custom bases. Enter any log equation and get the solution with detailed steps, domain analysis, and interactive graph.

Solve concentration and mixture word problems step by step. Blend two solutions, find how much stock to add for a target concentration, dilute with water, strengthen with pure solute, or drain and replace part of a mixture.

Plot polar equations interactively: r = sin(3t), Archimedean spirals, cardioids, limacons, lemniscates and butterfly curves, with adjustable range, resolution, palettes and grid. Overlay up to three equations and export SVG or PNG.

Factor polynomials using various methods including GCF, difference of squares, perfect square trinomials, sum/difference of cubes, and quadratic trinomials. Features step-by-step solutions, automatic pattern recognition, and verification.

Divide one polynomial by another using long division. Shows the complete step-by-step process, quotient, and remainder with detailed explanations.

Solve any quartic equation ax⁴+bx³+cx²+dx+e=0 using Ferrari's method. Get all four roots (real and complex), step-by-step solution, discriminant analysis, factored form, and interactive graph.

Solve equations containing radicals (square roots, cube roots, etc.) with step-by-step solutions. Automatically checks for extraneous solutions to ensure accuracy.

Simplify square roots and higher-order radicals into simplest radical form - sqrt(50) becomes 5*sqrt(2) - including rationalizing the denominator, with step-by-step solutions built on prime factorization.

Solve rational equations containing fractions with variables in the denominator. Get step-by-step solutions showing LCD calculation, fraction clearing, polynomial solving, and extraneous solution checks with interactive graphs.

Simplify, add, subtract, multiply, or divide rational expressions (fractions involving polynomials). Features step-by-step solutions, factoring visualization, domain analysis, and detailed explanations.

Use the Rational Root Theorem to find every possible rational root of a polynomial with integer coefficients. Enter the coefficients for the full candidate list, verification of the actual roots and step-by-step factoring.

Convert linear equations from standard form (Ax + By = C) to slope-intercept form (y = mx + b). Enter the equation or coefficients to get instant results with step-by-step solution, graph, and key line properties.

Divide polynomials by linear binomials (x - a) using the streamlined synthetic division method. Shows step-by-step process with coefficients and remainder.

Visualize the feasible region (solution set) for a system of two or more linear inequalities. Graph each inequality on a coordinate plane and identify the intersection region.

Solve systems of linear equations (2x2, 3x3, or larger) using Gaussian elimination, Cramer's Rule, or matrix methods. Features detailed step-by-step solutions and multiple solution approaches.

Solve systems of two or more nonlinear equations using the Newton-Raphson method. Find all solutions with step-by-step iterations, Jacobian matrix, convergence analysis, and interactive contour graph.

Solve classic two-train word problems step by step: trains meeting head-on, overtaking in the same direction, crossing each other with lengths, passing a pole, or crossing a platform, with animated track visuals and relative-speed maths.

Solve trigonometric equations step by step. Enter any trig equation like sin(x)=0.5 or 2cos(x)+1=0 and get all solutions in any interval, with unit circle visualization and interactive graph.

Calculate the vertex (maximum or minimum point) and the axis of symmetry for any quadratic function (parabola) with detailed step-by-step solutions.

Solve A-and-B-working-together rate problems in five forms: combined time, the missing solo time of one worker, fill-versus-drain pipes, alternating shifts, and partial completion when one worker joins midway. Fully explained.

Calculate the x-intercept (where the graph crosses the x-axis) and y-intercept (where the graph crosses the y-axis) of any equation with detailed step-by-step solutions.