Type any one-variable linear equation to see the correct worked solution, or drill an endless stream of practice problems with instant checking. Your score and streak are saved on this device.
Enter a one-variable linear equation, e.g. 3x + 5 = 20, and press Solve.
The equation solver, one-step and two-step practice, worked solutions and your local score & streak stay free forever. Pro unlocks:
Try it now with demo code AV-ALGEBRA-TRAINER-DEMO — or AV-ALL-DEMO for All-Access to every AppVitamins tool.
Algebra Trainer is a free tool for practicing one-variable linear equations — the foundation of high school algebra. Whether you're checking homework, studying for a test, or just want to see the reasoning behind a solution, the solver shows every step, and the practice generator gives you unlimited fresh problems with instant, correct checking.
Type any linear equation with a single variable, such as 3x + 5 = 20 or 5x - 4 = 2x + 11. The solver parses both sides of the equation, collects the variable terms onto one side and the constant numbers onto the other — exactly the way you'd solve it by hand — and shows each intermediate step with a plain-English note describing the operation performed. It correctly handles negative coefficients, decimals, variables on both sides, and the special cases of no solution and infinitely many solutions.
Every linear equation is really a statement that two expressions are equal, like a balanced scale. The golden rule of solving one is simple: whatever you do to one side, you must do to the other side too, or the scale tips. To isolate x, work backwards through the order of operations — undo addition or subtraction first, then undo multiplication or division last. That reverse order is exactly why 3x + 5 = 20 is solved by first subtracting 5 from both sides (giving 3x = 15), and only then dividing both sides by 3 (giving x = 5).
One-step equations like x + 7 = 12 or 4x = 20 need a single operation to solve and are the right place to build confidence. Two-step equations like 3x + 5 = 20 combine two operations and are the standard middle-school-to-high-school benchmark. Simultaneous (two-variable) equations, unlocked in Pro, involve two equations sharing two unknowns, x and y, solved together using elimination or substitution — a core Algebra 1 and Algebra 2 topic that bridges into systems of equations and, later, linear algebra.
Research on worked examples and retrieval practice consistently shows that immediate, specific feedback — not just "right" or "wrong," but the actual correct working — helps students catch and correct misconceptions faster than delayed feedback like a graded test days later. That's why every practice problem here can reveal its full step-by-step solution on demand, so a wrong answer becomes a mini-lesson instead of a dead end.
The single most common algebra mistake is a dropped or flipped negative sign when moving a term across the equals sign. Write out the "subtract b from both sides" step explicitly instead of skipping straight to the answer — it's slower at first but eliminates almost all sign errors within a few weeks of practice. Always substitute your final answer back into the original equation to confirm both sides match; this single habit catches the vast majority of careless mistakes before they cost you marks on a test.
Algebra Trainer is an educational practice tool, not a substitute for instruction from a qualified teacher. Always verify important homework or exam answers against your course materials.
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