Inequalities on a Number Line - Free Printable

Let’s go through each number line one by one and figure out what inequality it shows.

We look at two things:
1. Is the circle open (○) or closed (●)?
- Open circle means the number is not included → use < or >
- Closed circle means the number is included → use ≤ or ≥
2. Which way does the arrow point?
- Arrow to the left means “less than”
- Arrow to the right means “greater than”

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Problem 1:
- Circle is open at 6 → not including 6
- Arrow points left → less than
→ So, x < 6 ✔

Problem 2:
- Circle is closed at 14 → includes 14
- Arrow points right → greater than
→ So, x ≥ 14 ✔

Problem 3:
- Circle is open between 4 and 5 → that’s 4.5 (or 4½)
- Arrow points right → greater than
→ So, x > 4.5 or x > 4½ ✔

Problem 4:
- Circle is closed between 8 and 9 → that’s 8.5 (or 8½)
- Arrow points left → less than
→ So, x ≤ 8.5 or x ≤ 8½ ✔

Problem 5:
- Circle is open at -3 → not including -3
- Arrow points left → less than
→ So, x < -3 ✔

Problem 6:
- Circle is closed at 2 → includes 2
- Arrow points right → greater than
→ So, x ≥ 2 ✔

Problem 7:
- Circle is open between 4 and 5 → that’s 4.5 (or 4½)
- Arrow points left → less than
→ So, x < 4.5 or x < 4½ ✔

Problem 8:
- Circle is closed between -1 and 0 → that’s -0.5 (or -½)
- Arrow points left → less than
→ So, x ≤ -0.5 or x ≤ -½ ✔

All answers match what’s written on the sheet — so we’re good!

Final Answer:
1) x < 6
2) x ≥ 14
3) x > 4.5 or x > 4½
4) x ≤ 8.5 or x ≤ 8½
5) x < -3
6) x ≥ 2
7) x < 4.5 or x < 4½
8) x ≤ -0.5 or x ≤ -½