Math worksheet for practicing reading and representing inequalities using number lines.

Let's solve this step by step. The worksheet is divided into two sections:

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Section A: State the inequality represented on the number lines

We need to interpret each number line and write the correct inequality.

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1)
- Closed circle at 1, arrow going to the right.
- This means $ x \geq 1 $

✔ Answer: $ x \geq 1 $

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2)
- Open circle at 3, arrow going to the left.
- This means $ x < 3 $

✔ Answer: $ x < 3 $

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3)
- Open circle at -1, arrow going to the right.
- This means $ x > -1 $

✔ Answer: $ x > -1 $

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4)
- Closed circle at -3, arrow going to the right.
- This means $ x \geq -3 $

✔ Answer: $ x \geq -3 $

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5)
- Closed circle at -2, arrow going to the left.
- This means $ x \leq -2 $

✔ Answer: $ x \leq -2 $

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6)
- Open circle at -1, open circle at 2, shaded between them.
- This means $ -1 < x < 2 $

✔ Answer: $ -1 < x < 2 $

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7)
- Open circle at -2, closed circle at 1, shaded between them.
- This means $ -2 < x \leq 1 $

✔ Answer: $ -2 < x \leq 1 $

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8)
- Open circle at -4, open circle at 2, shaded between them.
- This means $ -4 < x < 2 $

✔ Answer: $ -4 < x < 2 $

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9)
- Closed circles at -3 and 2, shaded between them.
- This means $ -3 \leq x \leq 2 $

✔ Answer: $ -3 \leq x \leq 2 $

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10)
- Open circle at -3, closed circle at 1, shaded between them.
- This means $ -3 < x \leq 1 $

✔ Answer: $ -3 < x \leq 1 $

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✔ Section A Answers Summary:

| Question | Answer |
|--------|--------|
| 1) | $ x \geq 1 $ |
| 2) | $ x < 3 $ |
| 3) | $ x > -1 $ |
| 4) | $ x \geq -3 $ |
| 5) | $ x \leq -2 $ |
| 6) | $ -1 < x < 2 $ |
| 7) | $ -2 < x \leq 1 $ |
| 8) | $ -4 < x < 2 $ |
| 9) | $ -3 \leq x \leq 2 $ |
| 10) | $ -3 < x \leq 1 $ |

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Section B: Represent each inequality on the given number lines

Now we graph each inequality on a number line.

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1) $ x \geq -2 $
- Closed circle at -2, arrow going to the right.

✔ Draw: ● at -2 → arrow right

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2) $ x < 8 $
- Open circle at 8, arrow going to the left.

✔ Draw: ○ at 8 → arrow left

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3) $ x \leq 5 $
- Closed circle at 5, arrow going to the left.

✔ Draw: ● at 5 → arrow left

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4) $ x < -3 $
- Open circle at -3, arrow going to the left.

✔ Draw: ○ at -3 → arrow left

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5) $ x > 6 $
- Open circle at 6, arrow going to the right.

✔ Draw: ○ at 6 → arrow right

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6) $ 0 < x < 5 $
- Open circles at 0 and 5, shaded between them.

✔ Draw: ○ at 0, ○ at 5, line between them

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7) $ 2 < x \leq 3 $
- Open circle at 2, closed circle at 3, shaded between.

✔ Draw: ○ at 2, ● at 3, line between

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8) $ 7 < x < 10 $
- Open circles at 7 and 10, shaded between.

✔ Draw: ○ at 7, ○ at 10, line between

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9) $ -3 \leq x \leq 2 $
- Closed circles at -3 and 2, shaded between.

✔ Draw: ● at -3, ● at 2, line between

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10) $ -1 < x \leq 4 $
- Open circle at -1, closed circle at 4, shaded between.

✔ Draw: ○ at -1, ● at 4, line between

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✔ Section B Instructions (How to draw):

For each:
- Use closed circle (●) for $ \leq $ or $ \geq $
- Use open circle (○) for $ < $ or $ > $
- Draw a line (shading) in the direction of the inequality
- For compound inequalities, shade between two points

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Final Notes:

This worksheet tests understanding of:
- How to read number lines with inequalities
- How to represent inequalities visually
- The difference between open and closed circles
- Direction of shading based on inequality sign

Let me know if you'd like a visual representation or printable version!