Linear Equation Solver
Solve first-degree equations (ax + b = 0) instantly. Enter the coefficients and see the value of x with step-by-step solution.
Enter the coefficients of the equation ax + b = 0
How to solve a linear equation?
Every linear equation can be written as ax + b = 0 (with a ≠ 0). Isolating x gives you x = −b ÷ a.
With actual numbers it's easy to see. For 3x + 9 = 0, x = −9 ÷ 3, which works out to −3.
Linear (first-degree) equations
A first-degree equation has the form ax + b = 0 with a ≠ 0. Isolating x gives x = -b/a. Example: for 3x - 12 = 0, we get x = 12/3 = 4. The solution relies on two basic principles: the additive principle (adding the same value to both sides preserves equality) and the multiplicative principle (multiplying or dividing both sides by the same non-zero value preserves equality).
A system of two linear equations in two unknowns can be solved by substitution (isolate one variable and replace it in the other equation), addition/elimination (multiply one equation so coefficients cancel when added) or by the matrix form using Cramer's rule with determinants: x = D_x/D, y = D_y/D.
Applications and history
Linear equations model the rule of three, unit conversions, scale problems, mixture problems and any direct or inverse proportion. They already appeared in Egyptian papyri (Rhind, ~1650 BCE) and in the work of the Persian mathematician Al-Khwarizmi (~825 CE), whose book "Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala" gave us the word algebra (from al-jabr, "restoration" — moving terms to the other side of the equation).
FAQ
What if a = 0? Then the equation reduces to b = 0: if b is also zero, every real number is a solution; otherwise there is no solution.
What is the geometric meaning? The graph of y = ax + b is a straight line; the solution of ax + b = 0 is its x-intercept.
How do I check the answer? Substitute the value back into the original equation and verify that both sides match.
Why is "linear" the name? Because the unknown appears only with exponent 1 and the graph is a straight line — no curvature, no powers, no products of unknowns.
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Solve first-degree equations
Written as ax + b = 0, the first-degree equation opens the door to algebra and is the first kind of problem you tackle with a single unknown. Here you enter the coefficients a and b, and the value of x comes out already calculated.
It looks trivial, but isolating x without tripping up (moving b to the other side and dividing by a) is exactly where many beginning students go wrong. The math comes out right, which helps you check exercises, review for a test or solve any everyday linear equation.
Everything is processed in your own browser. Change the coefficients and the value of x recomputes on its own, so you can try several equations one after another.