Inequalities · Meet inequalities · 1.1

Inequality symbols.

An inequality compares two amounts that need not be equal. < means “less than”, > “greater than”, ≤ “at most / no more than” (includes the value), and ≥ “at least / no less than” (includes the value). The phrase tells you which symbol — and whether the boundary is included.

01 / THE IDEA

See it work.

Watch the method

Inequality symbols

“at least” → ≥, “at most” → ≤, “more than” → >, “less than” → <.

1 / 1
at least\text{at least}
1

Match the words to the symbol

“at least” → ≥, “at most” → ≤, “more than” → >, “less than” → <.

gege
— / WHY IT WORKS

The idea underneath.

Words → symbols

Translate the comparison phrase into a symbol, watching for whether the boundary counts.

Why it works

“At least 18” means 18 is allowed: ≥ 18.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Which symbol means “more than”?

1

Answer

>

EX 2medium

Which symbol means “less than”?

1

Answer

<

EX 3hard

Which symbol means “no less than”?

1

Answer

≥

04 / COMMON TRAPS

Where students slip.

Trap

Reading “at most” as <.

Fix

“At most” includes the value → ≤.

Trap

Pointing the symbol the wrong way.

Fix

The small end points at the smaller amount.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Which symbol means “no more than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
C2

Which symbol means “at most”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
C3

Which symbol means “more than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
C4

Which symbol means “at most”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
Apply

Apply (4)

A1

Which symbol means “more than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
A2

Which symbol means “no less than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
A3

Which symbol means “no more than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
A4

Which symbol means “no less than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
Extension

Extension (4)

E1

Which symbol means “at least”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
E2

Which symbol means “no less than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
E3

Which symbol means “less than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.
E4

Which symbol means “less than”?

Need a hint?
  • Does the boundary value count? Then use ≤ or ≥.
  • Match “more/less than” to >/<.