Let's solve each of the number line graphs and write the correct inequality for each. We'll go step by step, analyzing the direction of the shading and the type of dot (open or closed) at the endpoint.
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Key Rules:
-
Closed circle (●) means the endpoint is
included → use
≤ or
≥
-
Open circle (○) means the endpoint is
not included → use
< or
>
-
Shading to the left → values are
less than the point
-
Shading to the right → values are
greater than the point
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Now let’s analyze each graph:
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1. First row, left
- Open circle at
3
- Shading to the
left
- So:
x < 3
✔ Answer: x < 3
---
2. First row, right
- Open circle at
8
- Shading to the
right
- So:
x > 8
✔ Answer: x > 8
---
3. Second row, left
- Closed circle at
-5
- Shading to the
right
- So:
x ≥ -5
✔ Answer: x ≥ -5
---
4. Second row, right
- Closed circle at
1
- Shading to the
left
- So:
x ≤ 1
✔ Answer: x ≤ 1
---
5. Third row, left
- Open circle at
5
- Shading to the
left
- So:
x < 5
✔ Answer: x < 5
---
6. Third row, right
- Open circle at
-1
- Shading to the
right
- So:
x > -1
✔ Answer: x > -1
---
7. Fourth row, left
- Open circle at
10
- Shading to the
left
- So:
x < 10
✔ Answer: x < 10
---
8. Fourth row, right
- Open circle at
-2
- Shading to the
left
- So:
x < -2
✔ Answer: x < -2
---
9. Fifth row, left
- Closed circle at
-5
- Shading to the
left
- So:
x ≤ -5
✔ Answer: x ≤ -5
---
10. Fifth row, right
- Open circle at
-8
- Shading to the
right
- So:
x > -8
✔ Answer: x > -8
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✔ Final Answers:
1.
x < 3
2.
x > 8
3.
x ≥ -5
4.
x ≤ 1
5.
x < 5
6.
x > -1
7.
x < 10
8.
x < -2
9.
x ≤ -5
10.
x > -8
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Let me know if you'd like this formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of write inequalities worksheet.
