⚖️The Four Symbols
>Greater Than
Left side is BIGGER than the right.
The number on the line is NOT included.
x > 5 → 6, 7, 100… (not 5)
<Less Than
Left side is SMALLER than the right.
The number on the line is NOT included.
x < 5 → 4, 3, 0… (not 5)
≥Greater / Equal
Bigger OR equal to the right side.
The number on the line IS included.
x ≥ 5 → 5, 6, 7… (5 counts!)
≤Less / Equal
Smaller OR equal to the right side.
The number on the line IS included.
x ≤ 5 → 5, 4, 3… (5 counts!)
🐊 The hungry-mouth trick
The open mouth always gobbles the bigger number. The pointy end aims at the smaller one.
So 3 < 8 reads "three is less than eight." 👄
📏Graph It on a Number Line
Open circle ○
Leaves the number OUT. Use for < and >.
Closed circle ●
Fills it IN — the number counts. Use for ≤ and ≥.
✏️Read a Word Problem
🎢 The sign says: "You must be at least 48 inches tall to ride."
1Let h = your height in inches.
2"At least" means greater than or equal to → use the symbol ≥.
3Write the inequality: h ≥ 48.
4Graph it with a closed circle on 48 (because 48 IS allowed) and shade to the right.
✅ Answer: h ≥ 48 → 48", 49", 50"… all work. Exactly 48" can ride!
🔑Key Terms
⚖️Inequality A math sentence showing two values are NOT equal (<, >, ≤, ≥).
🎯Solution Set ALL the values that make the inequality true.
⭕Open Circle Marks a number that is NOT included (< and >).
🔵Closed Circle A filled dot showing the number IS included (≤ and ≥).
⬆️At Least Means "greater than or equal to" → use ≥.
⬇️At Most Means "less than or equal to" → use ≤.
⭐
Remember: an inequality stands for a whole RANGE of answers, not just one. "Or equal to" (≤, ≥) fills the dot in — plain < and > leave it open!