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Algebra Trainer · Mathematics · High School

Solve Linear Equations Step by Step

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.

Step-by-Step Equation Solver

Enter a one-variable linear equation, e.g. 3x + 5 = 20, and press Solve.

Working

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Try it now with demo code AV-ALGEBRA-TRAINER-DEMO — or AV-ALL-DEMO for All-Access to every AppVitamins tool.

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About Algebra Trainer

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.

How the Solver Works

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.

The Balance Method

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 vs. Two-Step vs. Simultaneous

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.

Why Practice with Instant Checking Helps

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.

Tips for Fewer Sign Errors

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.

Frequently Asked Questions

How do you solve a linear equation step by step?
Isolate the variable by undoing operations in reverse order. First move any variable terms to one side by adding or subtracting them from both sides. Then move constant numbers to the other side the same way. Finally, divide both sides by the coefficient in front of the variable. Whatever you do to one side, you must do to the other, to keep the equation balanced.
What is the difference between a one-step and a two-step equation?
A one-step equation needs only one operation to solve, such as x + 7 = 12 (subtract 7) or 4x = 20 (divide by 4). A two-step equation needs two operations, such as 3x + 5 = 20, where you first subtract 5 from both sides and then divide by 3.
What does it mean when an equation has no solution or infinite solutions?
If solving leads to a false statement like 0 = 5, the equation has no solution. If it leads to a true statement like 0 = 0, it's true for every value of x, so it has infinitely many solutions. This usually happens when the variable terms cancel out completely on both sides.
How do you solve simultaneous (two-variable) equations?
Use elimination (scale one or both equations so a variable's coefficients match, then add or subtract the equations to cancel it out) or substitution (solve one equation for a variable, then substitute that expression into the other). Both reduce the problem to a single one-variable equation.
Why do I need to check my algebra answer?
Substituting your answer back into the original equation confirms both sides are equal. This catches arithmetic slips like a sign error, and is exactly what teachers and exams expect you to show for full marks.
Is my score and progress saved anywhere?
Yes, but only on your own device. Your score, current streak, best streak and totals are stored in your browser's localStorage. Nothing is sent to a server, and clearing your browser data will reset them.
What is included in Algebra Trainer Pro?
The equation solver, one-step and two-step practice packs, step-by-step working and local score tracking are all free forever. Pro unlocks the simultaneous equations pack, a printable worksheet with an answer key, and a mixed exam-style challenge mode.

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