linear inequality

A linear equation asks “where is the line exactly level?”; a linear inequality asks “where is one side higher than the other?” Instead of pinning down a single balance point, it describes a whole stretch of values — everything to the left of some point, or everything to the right.

Formally it is like a linear equation but with =, replaced by one of <, ≤, >, or ≥, and the variable still appearing only to the first power. Solving it uses the same isolating moves as an equation, with one famous twist: when you multiply or divide both sides by a negative number, you must flip the inequality sign.

Because the answer is usually a range rather than a point, the solution is drawn as a ray or segment on a number line and written compactly in interval notation.