Every linear equation with one variable, no matter how it’s dressed up, comes down to the exact same two moves repeated until x is alone.
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Linear Equation Solver
Solve ax + b = cx + d with every algebra step shown, not just the final answer.
Runs entirely in your browser. Nothing you enter is sent anywhere.
The one move that solves every version of this equation
Whatever the numbers, the method never changes: get every x term onto one side and every plain number onto the other, then divide. That's it, that's the entire technique behind ax + b = cx + d, dressed up in different numbers each time. Once that move feels automatic, an equation with x on both sides stops looking any harder than one with x on just one side.
Linear equation solver FAQ
What form of equation does this solve?
Any linear equation that fits ax + b = cx + d, which covers the vast majority of one-variable linear equations you'll meet, including ones with x on both sides. Set a coefficient to 0 to drop that term entirely, for example b = 0 and c = 0 turns it into the simple ax = d.
What does it mean when there is "no solution"?
It happens when the x terms on both sides are identical (a equals c) but the constants are not (b does not equal d). After the x terms cancel, you're left with something like 5 = 9, which is never true no matter what x is, so no value of x satisfies the original equation.
What does "infinitely many solutions" mean?
This happens when both sides of the equation are actually the same expression (a equals c AND b equals d), like 3x + 2 = 3x + 2. Every value of x makes it true, because both sides were never really different equations to begin with.
Why show the steps instead of just x = answer?
The value of x tells you the answer to one specific equation. The steps, moving the x terms to one side and the constants to the other, then dividing, show the method that solves every equation of this shape, which is what actually transfers to the next problem that looks different.
Is this calculator private?
Yes. Every calculation runs in your browser. Nothing you enter is sent to a server.
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Balance, not magic
An equation is a statement that two things are equal, and every legal move keeps that balance: whatever you do to one side, you do to the other. Moving the x terms to one side and the plain numbers to the other isn’t a special trick, it’s just subtracting the same amount from both sides until only x is left on its own. Once that clicks, x on both sides of the equals sign stops being a special, scarier case.
When “solve for x” has no answer
Not every equation has a solution. If the x terms are identical on both sides but the constants aren’t, say 2x + 3 = 2x + 7, subtracting the x terms leaves 3 = 7, which is never true regardless of what x is. That’s a legitimate outcome called “no solution”, not a sign that something went wrong in the algebra.
When every number works
The opposite case is just as real: if both sides of the equation are actually the same expression written differently, every value of x makes it true, “infinitely many solutions.” This tends to happen when an equation was built by doing the same operation to both sides of an already-true statement, so recognizing it is more about noticing the equation was never really asking you to find one specific x.