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To solve the compound inequality \( 4 \leq 2x - 8 < 18 \), let's break it down step-by-step.

1. **Separate the Compound Inequality:**
   \[
   4 \leq 2x - 8 \quad \text{and} \quad 2x - 8 < 18
   \]

2. **Solve the First Inequality:** 
   \[
   4 \leq 2x - 8
   \]
   Add 8 to both sides:
   \[
   4 + 8 \leq 2x
   \]
   \[
   12 \leq 2x
   \]
   Divide both sides by 2:
   \[
   6 \leq x
   \]
   or equivalently,
   \[
   x \geq 6
   \]

3. **Solve the Second Inequality:** 
   \[
   2x - 8 < 18
   \]
   Add 8 to both sides:
   \[
   2x < 26
   \]
   Divide both sides by 2:
   \[
   x < 13
   \]

4. **Combine the Results:**
   Now we have:
   \[
   6 \leq x < 13
   \]

5. **Express in Interval Notation:**
   The solution in interval notation is:
   \[
   [6, 13)
   \]

Would you like more details or have any questions?

### Related Questions:
1. How do you solve compound inequalities with “or” instead of “and”?
2. What are the rules for combining intervals in compound inequalities?
3. How can we check if a solution to a compound inequality is correct?
4. What does it mean when the interval notation uses \( \infty \) or \( -\infty \)?
5. Can compound inequalities have solutions that are empty sets?

**Tip:** Remember, square brackets \([ ]\) indicate the endpoint is included, while parentheses \(( )\) mean it is not included in interval notation.

Solve the compound inequality: 4 ≤ 2x - 8 < 18. Enter the exact answer in interval notation.

Learn how to solve the compound inequality 4 ≤ 2x - 8 < 18 and express the solution in interval notation. This problem covers key algebra concepts, including inequality manipulation and interval notation. Ideal for students in Grades 7-9.

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