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).
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.
Frequently asked questions
What if a = 0?
What is the geometric meaning?
How do I check the answer?
Why is "linear" the name?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.