# >, <, ≥, ≤
Equations use `=`.
**Inequalities** compare:
- `>` greater than
- `<` less than
- `≥` greater than or equal
- `≤` less than or equal
`x > 3` means x can be 3.1, 4, 100… but **not** 3.
`x ≥ 3` includes 3.
## Read from the left
`5 > x` is the same idea as `x < 5` (the crocodile mouth still eats the larger number).
> The open mouth faces the **larger** side: `8 > 2`.
## Four comparison symbols
| Symbol | Words | Includes the edge? |
| --- | --- | --- |
| > | greater than | no |
| < | less than | no |
| ≥ | at least / not less than | yes |
| ≤ | at most / not greater than | yes |
### Height-limit story
A ride says “height ≥ 120 cm”.
120 cm may ride. 119 may not.
A ride that said “height > 120” would refuse 120 cm. That extra line under the symbol matters in real life too.
### Mouth trick
The open mouth eats the larger number: `8 > 2`.
What if both sides are not equal — on purpose?
By the end of this lesson
Read >, <, ≥, ≤ and decide whether a given number is allowed (including the equal cases).
Remember
- > greater than (not equal). < less than (not equal).
- ≥ greater than or equal (includes the number). ≤ includes the number.
- x > 3 allows 3.1, 4, 100 — not 3.
- x ≥ 3 allows 3 as well.
- The open mouth faces the larger side: 8 > 2.
Worked examples
Cover the answer. Try the steps on paper, then open them.
Example 1 — Does 3 belong?
Is x = 3 allowed in x > 3? In x ≥ 3?
- x > 3: no, because equal is forbidden
- x ≥ 3: yes
Answer: no ; yes
Check: The extra line under > is the “or equal”.
Example 2 — Read both ways
5 > x means the same as x < 5.
- x is on the smaller side.
- x can be 4, 0, −2, not 5, not 6.
Answer: x < 5
Check: Flip the whole sentence carefully.
Example 3 — True or false
Is 8 > 2 true? Is −1 > 4 true?
- 8 is to the right of 2 → true
- −1 is to the left of 4 → false
Answer: true ; false
Check: Right on the number line is larger.
Common mistakes
Slip x > 3 includes 3.
Fix Only ≥ includes 3.
The line under the symbol is the equal.
Slip Thinking −1 > 4 because 1 looks smaller than 4 without the minus.
Fix −1 is less than 4.
Negatives sit to the left.
Slip Reading 5 > x as x > 5.
Fix 5 is the larger one, so x is smaller: x < 5.
Mouth eats the larger.
Try on paper first
Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.
1. Does x > 10 allow 10?
Answer: No
2. Does x ≤ 10 allow 10?
Answer: Yes
3. Does x < 0 allow −2?
Answer: Yes
4. Rewrite 7 > x with x on the left.
Answer: x < 7
Touch practice
8 tap / typeTap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.
Optional picture lab
After practiceReal world
Height limits and age limits.
Connect
if (score >= 40) pass.
⭐ Star quiz
9 questionsFinish the touch practice first if you can. Then answer without peeking. Read every “why”.