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Free Online Linear Equation Solver With Every Step Shown

Type a linear equation the way you would write it, with brackets and fractions, and get the answer with every step of the rearranging written out. The answer is substituted back into your original equation as a check, and the two cases with no solution or infinitely many are explained rather than reported as errors.

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Free Online Linear Equation Solver With Every Step Shown

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🟰 Linear Equation Solver Type it as you write it · every step shown · checked by substitution

The sum runs in your browser. Nothing you type is sent anywhere.

🟰 The equation

Write it as you would on paper. Brackets, fractions and x on both sides are all fine. Multiplication can be left out, so 3x and 2(x+1) both work.

Equation

Insert

Try one of these

The fifth and sixth are the two cases where other solvers say "error" instead of giving you the answer.

The answer

—

As a fraction—

Tidied to one side—

Left side at that value—

Right side at that value—

Each rearranging step, with what was done to both sides. The last row puts the answer back into your own equation.

Step	The equation now	What was done

Recent equations, kept in this browser only.

Nothing here yet Press Log to history on the Solve tab to keep an equation here.

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How to Solve a Linear Equation

Three steps, and the third is the one worth doing.

Type the equation the way you write it Brackets, fractions and the unknown on both sides are all fine, and the multiplication sign can be left out. There is no need to rearrange it first or split it into coefficients.

Read the answer, and the fraction form Where the answer is not a whole number the exact fraction is given alongside the decimal, because three sevenths is a better answer than 0.428571.

Check the substitution rows Both sides of your original equation are worked out at the answer. They should come to the same number, and seeing that is a stronger check than trusting the rearranging.

What to Know About Linear Equations

The two answers that are not numbers, and why they are answers.

No solution is an answer, not an error. In x + 1 = x + 2 the x cancels from both sides and leaves one equals two, which is never true, so there is no value of x that works. That is a complete and correct answer to the question. Solvers that return an error here are reporting their own confusion as a fault in your equation.

And so is every number. In 2(x + 1) = 2x + 2 both sides are the same expression written differently, so every value of x satisfies it. This is called an identity. Again the correct answer is not a number but a statement about all numbers, and it is named here rather than refused.

If it stops being linear, you are told. Multiplying two unknowns together, as in x*x or (x+1)(x+2), makes the equation quadratic, and dividing by an unknown makes it something else again. This page solves linear equations, and when yours is not one it says which thing made it non linear rather than quietly computing something else.

The answer is checked by substitution, not by trust. Both sides of your original equation are evaluated at the answer and shown. If the rearranging had gone wrong, those two numbers would differ, so this is an independent check rather than a repeat of the same calculation. It is the step most people skip and the only one that catches a mistake.

A fraction is given when the answer is not whole. Seven x equals three gives three sevenths, and that is shown as a fraction as well as 0.428571. The fraction is the exact answer; the decimal is a rounded version of it. For anything you are going to use in further algebra, the fraction is the one to carry forward.

It runs in your browser with nothing uploaded. The parser and the arithmetic are in the page, so it works offline once loaded and nothing you type is sent anywhere.

Key Features & Capabilities

What it does, and what it deliberately does not.

Type it as you write it Brackets, fractions, implied multiplication and the unknown on both sides, with no need to rearrange first.

Every step written out What was done to both sides at each stage, so it can be copied as a method rather than just an answer.

Substitution check Both sides of your own equation evaluated at the answer, which catches a mistake the rearranging would hide.

Handles the two odd cases No solution and every number are named and explained instead of being reported as errors.

Mistakes get a caret A real parser means the exact character causing the problem is pointed at and the reason named.

Nothing is uploaded It all runs in this tab and keeps working with the network off.

About Linear Equations

A linear equation is one where the unknown appears by itself, never squared, never multiplied by another unknown, never underneath a division. Solving one is the first piece of real algebra anybody learns, and the method is always the same: collect the unknowns on one side, collect the numbers on the other, divide by what is left in front of the unknown.

Most solvers ask you to put the equation into a particular form first, or to type coefficients into separate boxes. That is the wrong way round, because converting your equation into their form is where the sign errors happen, and sign errors are the whole difficulty of this topic. So here you type what you would have written on paper, with the brackets still in it, and the parser does the collecting.

The part worth dwelling on is that two of the possible answers are not numbers. If the unknown cancels from both sides and leaves something false, like one equals two, then no value works and the honest answer is that there is no solution. If it cancels and leaves something true, like zero equals zero, then every value works and the equation is an identity. Both of these are complete answers to a perfectly sensible question, and a great many calculators return an error for them, which teaches people that they have done something wrong when they have not.

The last decision is the substitution check. Every step of rearranging is shown, which is useful for homework, but showing the working does not prove the working. Putting the answer back into the original equation and evaluating both sides does, because it uses the equation you typed rather than the one the solver derived. If a sign went astray anywhere, those two numbers disagree and you can see it immediately.

Frequently Asked Questions

Brackets, fractions, no solution and infinitely many.

Yes. Brackets nest as deep as you like, division by a number is fine, and the multiplication sign can be left out, so 3x and 2(x+1) both work. You do not need to expand or rearrange anything first.

That the unknown cancelled from both sides and left a false statement, such as one equals two. No value of x can make the equation true, which is a complete answer rather than an error.

That both sides are the same expression written differently, so the equation is true whatever x is. This is called an identity. 2(x+1) = 2x+2 is the simplest example.

Because that is a quadratic, not a linear equation, and it has two answers rather than one. The quadratic equation solver on this hub handles it. This page tells you what made your equation non linear rather than silently solving something else.

Yes. Any single letter works, and the answer is given in terms of whichever one you used. If you type two different letters the page will tell you, because one equation with two unknowns has no single answer.

Because the fraction is exact and the decimal is rounded. Seven x equals three gives three sevenths, which is more useful than 0.428571 if the answer feeds into anything else.

No. The parser and the arithmetic both run in your browser, so nothing you type leaves the page and it works offline.