Less than or equal to sign ≤

x ≤ 10 means x can be 10 or anything below it. The open side of the sign always faces the larger value.

In word problems, these phrases translate to ≤:

• at most: “You can bring at most 2 bags” → bags ≤ 2
• no more than: “The load is no more than 1,500 lb” → load ≤ 1,500
• maximum, up to, not to exceed: “Speed limit 65 mph” → speed ≤ 65

On a number line, ≤ gets a closed (filled) dot at the boundary, because the boundary value is included. In interval notation, x ≤ 10 is (−∞, 10], with a square bracket on the included end.

• < means strictly less than: x < 10 excludes 10. Mixing up < and ≤ is a classic source of off-by-one errors in code and in eligibility rules.
• ⩽ (slanted) means the same as ≤ and is the usual form in some European countries. In LaTeX, the amssymb package provides it as \leqslant.
• ≦ (with a double bar) also means the same thing and is often seen in Japanese texts.

Use one form consistently in a document. For US readers, ≤ is the familiar one.

• Programming: <= in Python, JavaScript, C, Java and SQL. The reversed =< is a syntax error in most languages.
• Excel and Google Sheets: =IF(A1<=100, "OK", "Over"). Formulas don’t accept ≤, though you can use it as text in a label.
• Word: in an equation (Alt+=), type \le or \leq and press space.
• LaTeX: \le or \leq.
• Coding fonts with ligatures may draw <= as ≤ on screen, but the file still contains two characters.

In HTML, the less-than character starts a tag, so the two-character version needs escaping in markup. The single ≤ character doesn’t.