What each inequality symbol means
An inequality compares two values. There are five signs you will meet in school math: < less than, > greater than, ≤ less than or equal to, ≥ greater than or equal to, and ≠ not equal to. Read them from left to right: x < 7 means "x is less than 7".
< and > are strict inequalities: the two sides can never be equal. ≤ and ≥ also allow equality, which is why word problems use them for phrases like "at least" (≥) and "at most" or "no more than" (≤). The not equal sign ≠ only says the values differ; it does not say which one is bigger.
The other grids hold the advanced signs. ≪ and ≫ mean "much less than" and "much greater than", common in physics approximations. Slashed signs like ≮ and ≱ negate a comparison, and ⩽ ⩾ are slanted versions of ≤ ≥ that some textbooks prefer.
How to remember which way they point
The open side of < and > always faces the bigger number, and the point aims at the smaller one. Many teachers draw the sign as a hungry alligator that always eats the larger amount: in 9 > 4 the mouth opens toward 9.
Another trick: the less than sign < looks like a tilted capital L, for "less". For a closer look at each sign, see the greater than symbol and less than symbol pages.
Graphing and solving inequalities
On a number line, draw an open circle for < and > (the endpoint is not included) and a filled circle for ≤ and ≥ (it is included). Interval notation follows the same rule: x > 2 becomes (2, ∞), while x ≤ 5 becomes (−∞, 5] with a square bracket.
When you multiply or divide both sides by a negative number, flip the sign: −2x < 6 turns into x > −3. On a coordinate plane, strict inequalities get a dashed boundary line, and ≤ or ≥ get a solid one.
How to type inequality symbols
< and > are on every keyboard: Shift + comma and Shift + period on US layouts. On a Mac, press Option + , for ≤, Option + . for ≥ and Option + = for ≠. On Windows, hold Alt and type 243 for ≤ or 242 for ≥ on the number pad.
In LaTeX, use \leq, \geq, \neq, \ll and \gg. In spreadsheets and code, type the two-character versions <=, >= and != (or <> in Excel). The not equal symbol page lists the spelling for each language.