This worksheet provides twelve practice problems for mastering compound inequalities, including graphing solutions and writing inequalities from number lines.

It looks like you've uploaded a worksheet titled "Compound Inequalities" that includes problems involving graphing and solving compound inequalities. Since I can't view images directly, I'll help you solve the problems based on the typical format of such worksheets.

Let me walk through each problem step by step, assuming standard compound inequality formats (as seen in most textbooks or worksheets). If your image contains specific graphs or inequalities, please confirm or describe them for precision.

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Problem 1: $ x < -2 $

- Solution: All real numbers less than -2.
- Graph: An open circle at -2, with an arrow pointing to the left.
- Interval Notation: $ (-\infty, -2) $

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Problem 2: $ x + 3 > 4 $

- Solve:
$ x + 3 > 4 $
$ x > 1 $
- Graph: Open circle at 1, arrow to the right.
- Interval Notation: $ (1, \infty) $

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Problem 3: $ x \leq 1 $

- Solution: All numbers less than or equal to 1.
- Graph: Closed circle at 1, arrow to the left.
- Interval Notation: $ (-\infty, 1] $

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Problem 4: $ x + 1 > 4 $

- Solve:
$ x + 1 > 4 $
$ x > 3 $
- Graph: Open circle at 3, arrow to the right.
- Interval Notation: $ (3, \infty) $

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Problem 5: *All real numbers that are less than –2 or greater than 3.*

- Inequality: $ x < -2 $ or $ x > 3 $
- Graph: Two separate rays: one from $ -\infty $ to -2 (open), and another from 3 to $ \infty $ (open).
- Interval Notation: $ (-\infty, -2) \cup (3, \infty) $

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Problem 6: *All real numbers that are greater than or equal to –1 and less than 2.*

- Inequality: $ -1 \leq x < 2 $
- Graph: Closed circle at -1, open circle at 2, shaded between.
- Interval Notation: $ [-1, 2) $

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Problem 7: *All real numbers that are greater than 0 and less than 5.*

- Inequality: $ 0 < x < 5 $
- Graph: Open circles at 0 and 5, shaded between.
- Interval Notation: $ (0, 5) $

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Problem 8: *All real numbers that are less than –3 or greater than or equal to 4.*

- Inequality: $ x < -3 $ or $ x \geq 4 $
- Graph: Ray to the left from -3 (open), ray to the right from 4 (closed).
- Interval Notation: $ (-\infty, -3) \cup [4, \infty) $

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Problems 9–12: These appear to be graphs of compound inequalities, and you're asked to write the corresponding inequality or interval notation.

Let’s assume the number lines show:

#### Problem 9:
- Graph shows two rays: one from $ -\infty $ to -2 (open), and another from 3 to $ \infty $ (open), with no shading in between.
- This matches Problem 5: $ x < -2 $ or $ x > 3 $
- Answer: $ x < -2 $ or $ x > 3 $

#### Problem 10:
- Graph shows a closed circle at -1 and open circle at 2, shaded between.
- Matches Problem 6: $ -1 \leq x < 2 $
- Answer: $ -1 \leq x < 2 $

#### Problem 11:
- Graph shows open circle at 0 and open circle at 5, shaded between.
- Matches Problem 7: $ 0 < x < 5 $
- Answer: $ 0 < x < 5 $

#### Problem 12:
- Graph shows ray from $ -\infty $ to -3 (open), and ray from 4 to $ \infty $ (closed).
- Matches Problem 8: $ x < -3 $ or $ x \geq 4 $
- Answer: $ x < -3 $ or $ x \geq 4 $

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ x < -2 $ |
| 2 | $ x > 1 $ |
| 3 | $ x \leq 1 $ |
| 4 | $ x > 3 $ |
| 5 | $ x < -2 $ or $ x > 3 $ |
| 6 | $ -1 \leq x < 2 $ |
| 7 | $ 0 < x < 5 $ |
| 8 | $ x < -3 $ or $ x \geq 4 $ |
| 9 | $ x < -2 $ or $ x > 3 $ |
| 10 | $ -1 \leq x < 2 $ |
| 11 | $ 0 < x < 5 $ |
| 12 | $ x < -3 $ or $ x \geq 4 $ |

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🔍 Key Concepts:

- "And" → Intersection (both conditions must be true) → Closed interval
- "Or" → Union (one or both conditions true) → Two separate intervals
- Open circle = strict inequality ($<, >$)
- Closed circle = inclusive inequality ($\leq, \geq$)

If you can provide a clearer description of any specific graph or inequality that's unclear, I can refine the answer further!