A worked example: 2x + 4 = 0
Solving 2x + 4 = 0 gives x = −2 — subtract 4 from both sides to get 2x = −4, then divide by 2.
The formula: x = −b ÷ a
For any equation in the form ax + b = 0, isolating x always follows the same two moves: move b to the other side (making it −b), then divide by a. This single formula handles every linear equation in one variable, once it's in standard form.
Rearranging a messier equation first: 3x = 9 − x
An equation not already in ax + b = 0 form needs rearranging before the formula applies — 3x = 9 − x becomes 4x − 9 = 0 by moving the −x to the left side, giving a = 4, b = −9 and a solution of x = 2.25.
Why coefficient a can never be zero
If a were 0, the equation would just be b = 0 — either always true (if b is also 0) or never true (if b isn't), but never a statement about x at all. The equation stops being "linear in x" the moment its x-coefficient vanishes.
What comes next: two equations, two unknowns
A single linear equation in one variable, like this one, is the simplest case — a system of two such equations sharing two unknowns (x and y) needs a different technique entirely, since one equation alone can't pin down two unknowns.