Linear equation with one unknown

A linear equation of the form ax + b = 0 is the simplest kind of algebraic equation, one in which the unknown appears only to the first power — never squared, under a root, or in a denominator. The letters a and b are known numbers called coefficients, x is the unknown we want to find, and the whole statement asserts that a certain expression equals zero. As long as a is not equal to zero, such an equation has exactly one solution, called its root, which is the single value of x that makes the two sides balance. Because its graph is a straight line, changing x produces a proportional, perfectly predictable change in the result, and the line crosses the horizontal axis at precisely that one root.

Linear equations are the workhorses of everyday mathematics: they model situations where quantities grow or shrink at a constant rate, such as converting units, splitting costs, computing speed or interest, or finding a break-even point. They also form the foundation for more advanced topics, since solving systems of them underpins much of algebra, physics, economics, and engineering. Mastering this basic case teaches the core habit of isolating the unknown by performing the same operation on both sides, a technique that carries over to nearly every equation you will ever meet.