Linear Equation Solver
Linear Equation Solver
Enter the coefficients a, b, and c from your linear equation in the form ax + b = c. This isolates x and gives you the solution, correctly flagging the special cases where a is zero.
"Linear" here means x appears only to the first power — no x², no roots of x — which is exactly why the equation graphs as a straight line rather than a curve. The special case where a equals zero is worth flagging separately: the equation reduces to just "b = c," which is either true for every value of x (infinitely many solutions) or false for all of them (no solution at all), rather than pointing to one specific answer the way a normal linear equation does.
- Formula: x = (c − b) ÷ a — subtract b from both sides, then divide by a to isolate x.
- What "linear" means here: the variable x appears only to the first power (no x², no roots of x), which is why the equation graphs as a straight line.
- Special case when a = 0: the equation reduces to just "b = c" — if that's true, every value of x works (infinite solutions); if it's false, no value of x works (no solution).
What does it mean if the calculator says "infinite solutions"?
This happens when a = 0 and b already equals c, meaning the x term vanished from the equation entirely and what remains is always true, regardless of what x is.
What does it mean if the calculator says "no solution"?
This happens when a = 0 but b doesn't equal c — the x term vanishes, leaving a false statement (like 3 = 7) that can't be satisfied by any value of x.
Linear Equation Solver
Enter the coefficients a, b, and c from your linear equation in the form ax + b = c. This isolates x and gives you the solution, correctly flagging the special cases where a is zero.
"Linear" here means x appears only to the first power — no x², no roots of x — which is exactly why the equation graphs as a straight line rather than a curve. The special case where a equals zero is worth flagging separately: the equation reduces to just "b = c," which is either true for every value of x (infinitely many solutions) or false for all of them (no solution at all), rather than pointing to one specific answer the way a normal linear equation does.
- Formula: x = (c − b) ÷ a — subtract b from both sides, then divide by a to isolate x.
- What "linear" means here: the variable x appears only to the first power (no x², no roots of x), which is why the equation graphs as a straight line.
- Special case when a = 0: the equation reduces to just "b = c" — if that's true, every value of x works (infinite solutions); if it's false, no value of x works (no solution).
What does it mean if the calculator says "infinite solutions"?
This happens when a = 0 and b already equals c, meaning the x term vanished from the equation entirely and what remains is always true, regardless of what x is.
What does it mean if the calculator says "no solution"?
This happens when a = 0 but b doesn't equal c — the x term vanishes, leaving a false statement (like 3 = 7) that can't be satisfied by any value of x.