Printable math worksheet for writing inequalities based on number line graphs.

Let's solve each of the 10 number line graphs and write the correct inequality that describes each one.

We need to interpret:
- Open circle → strict inequality: `>` or `<`
- Closed (filled) circle → inclusive inequality: `≥` or `≤`
- Direction of the arrow tells us whether it's greater than or less than.
- The point where the shading starts is the boundary value.

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1)

- Open circle at -4, shaded to the right
- So, values greater than -4
- Inequality: $ x > -4 $

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2)

- Open circle at -30, shaded to the right
- So, values greater than -30
- Inequality: $ x > -30 $

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3)

- Open circle at -24, shaded to the right
- So, values greater than -24
- Inequality: $ x > -24 $

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4)

- Open circle at -12, shaded to the right
- So, values greater than -12
- Inequality: $ x > -12 $

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5)

- Closed circle at 10, shaded to the right
- So, values greater than or equal to 10
- Inequality: $ x \geq 10 $

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6)

- Open circle at -54, shaded to the right
- So, values greater than -54
- Inequality: $ x > -54 $

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7)

- Open circle at -18, shaded to the right
- So, values greater than -18
- Inequality: $ x > -18 $

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8)

- Open circle at -2, shaded to the right
- So, values greater than -2
- Inequality: $ x > -2 $

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9)

- Open circle at -36, shaded to the right
- So, values greater than -36
- Inequality: $ x > -36 $

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10)

- Open circle at -3, shaded to the right
- So, values greater than -3
- Inequality: $ x > -3 $

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✔ Final Answers:

| Number | Inequality |
|--------|--------------------|
| 1) | $ x > -4 $ |
| 2) | $ x > -30 $ |
| 3) | $ x > -24 $ |
| 4) | $ x > -12 $ |
| 5) | $ x \geq 10 $ |
| 6) | $ x > -54 $ |
| 7) | $ x > -18 $ |
| 8) | $ x > -2 $ |
| 9) | $ x > -36 $ |
| 10) | $ x > -3 $ |

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🔍 Explanation Summary:

- Open circles mean the endpoint is not included, so use `>` or `<`.
- Closed circles mean the endpoint is included, so use `≥` or `≤`.
- Arrows pointing right → greater than (`>`, `≥`)
- Arrows pointing left → less than (`<`, `≤`)

All these graphs have arrows pointing to the right, so all are "greater than" inequalities.

Only #5 has a closed circle, so it’s ≥. All others are open circles → >.

✔ All answers are consistent with the visual representation.

Let me know if you'd like this formatted as a printable answer sheet!