Linear equation solver
One variable, first power: expand, collect, divide. Every move shown on its own line.
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What counts as a linear equation?
A linear equation has the variable only to the first power, with no x², no x under a root and no x in a denominator. It always has exactly one solution, no solution, or every real number as a solution.
Graphically, each side is a straight line, and the solution is the x-coordinate where the two lines cross.
How to solve a linear equation
- Expand any brackets on both sides.
- If there are fractions or decimals, multiply both sides by a number that clears them (the LCD, or 10, 100…).
- Combine like terms on each side.
- Move every variable term to one side and every constant to the other by adding or subtracting.
- Divide both sides by the coefficient of the variable.
- Substitute your answer into the original equation to check it.
Frequently asked questions
What makes an equation linear?
The variable appears only to the power 1 and is never multiplied by itself, placed under a root or used in a denominator. 3x + 2 = 11 is linear; x² = 9 and 1/x = 2 are not.
Can a linear equation have no solution?
Yes. If the variable cancels and you are left with something false, like 0 = 5, there is no solution; the two sides are parallel lines. If you are left with something true, like 4 = 4, every real number works.
How do I handle decimals?
Multiply both sides by 10, 100 or 1000 to turn them into whole numbers first. EquationCraft converts decimals to exact fractions automatically, so 0.3 is treated as 3/10.