Greater than or equal to sign (≥): every inequality symbol (>, <, ≥, ≤, ≠, ≈) with what it means, how to type each one on Windows, Mac, phones, Word, Google Docs, Excel and LaTeX, the words that mean each symbol ("at least", "no more than"), how to read an inequality on a number line, the rules for solving one, and a printable symbols chart with practice

"Greater than or equal to sign" is searched sixty thousand times a month in the United States, and for three different reasons: a child in grade 1 learning which way the crocodile faces, a student in grade 6 or 7 meeting x ≥ 5 for the first time, and an adult who needs to type ≥ in a document and cannot find it on the keyboard. This page answers all three. The chart has every inequality symbol with its meaning and the key presses that produce it on each device; the sections after it cover the words that mean each symbol, how to read an inequality on a number line, and the rules for solving one. The printable has the chart and a page of practice with answers.

Download the inequality symbols chart and practice sheet (PDF) (the eight symbols with meanings, Unicode, HTML, LaTeX and the Windows, Mac, Word and Docs key presses; the words-to-symbols table; number-line rules; the flip rule; twelve practice questions with answers; two pages, free).

The greater than or equal to sign

The sign is ≥: a greater-than sign (>) with a line under it. The line means "or equal to". So:

• x > 5 means x is greater than 5: 5.1, 6, 100, but not 5 itself.
• x ≥ 5 means x is greater than or equal to 5: 5 counts, and so does everything above it.
• x < 5 means x is less than 5; x ≤ 5 means x is less than or equal to 5.

The symbol is read aloud as "greater than or equal to" (in Britain also "more than or equal to"), and its official name in Unicode is GREATER-THAN OR EQUAL TO, code point U+2265. In some British and French textbooks the line under it is slanted (⩾, U+2A7E); it means exactly the same thing.

Every inequality symbol: the chart

Two that look like inequalities but are not: = (equal) and ≡ (identical to, used for identities such as (a + b)² ≡ a² + 2ab + b²).

How to type each symbol

The number-pad Alt codes need the number pad, not the row of numbers above the letters; on a laptop without one, Word's code-then-Alt+X method or the Windows emoji panel (Windows key + .) with its Symbols tab works. On a Mac, the Character Viewer (Control+Command+Space) finds any of them by name. In spreadsheets and code the two-character forms >= and <= are the only ones that work; the single ≥ character is not an operator there.

Which way does the sign go

The wide, open end of > or < faces the bigger number, and the point faces the smaller one: 9 > 4, 4 < 9. The usual way to teach it is the crocodile (or alligator, or Pac-Man) that opens its mouth towards the bigger meal. Another: the sign is a squashed arrow that points at the smaller number. Either way, the test is to read the sentence aloud from left to right and ask whether it is true: "nine is greater than four" is true, so 9 > 4 is written correctly.

A sentence can be read in both directions. 5 > x says the same as x < 5: x is less than 5. In algebra the variable is usually put on the left, so x < 5 is the normal form.

The words that mean each symbol

Word problems and real rules hide the symbols inside phrases. These are the ones that matter:

The two that cause the most lost marks are "at least" (the number itself counts) and "more than" (it does not). A speed limit of 65 means speed ≤ 65; the pass mark of 40 means marks ≥ 40; "fewer than 10 items" at the express checkout means items < 10, so 10 is too many.

Reading an inequality on a number line

An inequality in one variable is a set of numbers, and the number line shows it:

• Draw a circle at the boundary number. Filled (closed) circle for ≥ or ≤, because the number is included; empty (open) circle for > or <, because it is not.
• Shade or draw an arrow in the direction of the solutions: to the right for "greater", to the left for "less".

So x ≥ 5 is a filled circle at 5 with an arrow to the right; x < 5 is an open circle at 5 with an arrow to the left; −2 < x ≤ 3 is an open circle at −2, a filled circle at 3, and the segment between them shaded.

In interval notation the same sets are [5, ∞), (−∞, 5) and (−2, 3]: a square bracket includes the end, a round bracket excludes it, and infinity always gets a round bracket.

Solving an inequality: the rules

An inequality is solved like an equation, with one extra rule.

1. Add or subtract the same number on both sides: the sign stays. From x + 3 ≥ 10, subtract 3: x ≥ 7.
2. Multiply or divide both sides by a positive number: the sign stays. From 3x < 12, divide by 3: x < 4.
3. Multiply or divide both sides by a negative number: the sign flips. From −2x > 6, divide by −2: x < −3. (Check with a number: x = −4 gives −2 × −4 = 8, and 8 > 6 is true.)
4. Swap the sides: the sign flips. 5 > x becomes x < 5.

Why the flip: multiplying by a negative mirrors the number line, so the bigger number becomes the smaller one. 2 < 3, but −2 > −3.

Two worked examples in the exam style:

• Solve 4x − 7 ≤ 9. Add 7: 4x ≤ 16. Divide by 4: x ≤ 4. On a number line: filled circle at 4, arrow left.
• Solve 5 − 3x < 20. Subtract 5: −3x < 15. Divide by −3 and flip: x > −5. Check x = 0: 5 − 0 = 5, and 5 < 20 is true.

The integers that satisfy an inequality are a common question: the integers with −2 < x ≤ 3 are −1, 0, 1, 2, 3 (five of them; −2 is excluded by the open end).

Where it sits in school

In the United States, comparing numbers with >, < and = begins in grade 1 (Common Core 1.NBT.3) and is drilled through grade 4 with decimals and fractions; writing inequalities such as x > c for real-world conditions is grade 6 (6.EE.8); solving one-step and two-step inequalities, with the flip rule, is grade 7 (7.EE.4b); compound inequalities and inequalities in two variables are Algebra 1. In England, Year 2 orders numbers with <, > and =, and solving linear inequalities is Key Stage 3 and GCSE. In the CBSE curriculum the symbols come in the primary classes and Linear Inequalities is a Class 11 chapter. In Australia, comparing and ordering is Year 2 and 3 and inequalities are Year 10.

Practice: twelve questions

Write the inequality (1 to 4), say whether it is true or false (5 to 8), solve (9 to 12).

1. A film is for people aged 15 or over.
2. The lift holds at most 8 people.
3. A number is more than 20 and less than 30.
4. The temperature stayed under 0 °C.
5. 0.5 ≥ 1/2
6. −3 > −2
7. 7 ≤ 7
8. 2/3 < 0.6
9. x − 4 > 1
10. 2x + 1 ≤ 9
11. −x ≥ 3
12. 10 − 2x < 4

Answers: 1) age ≥ 15. 2) people ≤ 8. 3) 20 < n < 30. 4) T < 0. 5) True (0.5 equals 1/2, and "or equal" allows it). 6) False (−3 is further left). 7) True. 8) False (2/3 is 0.667). 9) x > 5. 10) x ≤ 4. 11) x ≤ −3 (divided by −1, so the sign flipped). 12) −2x < −6, so x > 3 (flipped).

Download the inequality symbols chart and practice sheet (PDF)

Where to get help

A 1-on-1 online maths class with a tutor who holds a master's in mathematics, for grades 1 to 8 in the US curriculum and the equivalent years in England, Australia and CBSE: comparing numbers with real objects on the shared screen for the youngest, the number line and the flip rule for the older ones, then the word problems the tests use. The recording and notes after every class, the same tutor every week, US$10 to $13 an hour. The grade 6 math page has the grades; the free 30-minute first class is a real lesson, usually on the homework the child brings.

Questions parents ask

See how we teach this, 1-on-1 online →