inequality symbol

Equality says two numbers are the same; an inequality symbol says one is bigger or smaller than the other. The two main signs are < (“less than”) and > (“greater than”). A handy memory trick: the symbol is like a hungry mouth that always opens toward the larger number, so 2 < 5 and 5 > 2 both say the same thing.

There are five symbols in common use: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), and ≠ (not equal to). The bar underneath in ≤ and ≥ adds the possibility of equality, which matters when a boundary value should be allowed. So x ≤ 3 includes 3 itself, but x < 3 does not.

Inequality symbols express the order relation among real numbers and are read left to right: a < b means a is to the left of b on the number line. One rule trips up beginners: when you multiply or divide both sides of an inequality by a negative number, you must flip the symbol’s direction, so −2x < 6 becomes x > −3.