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To solve the compound inequality:

\[
4 \leq 2x - 8 < 18
\]

we will break it into two separate inequalities and solve each one individually.

### Step 1: Solve \( 4 \leq 2x - 8 \)

1. Add 8 to both sides:
   \[
   4 + 8 \leq 2x
   \]
   \[
   12 \leq 2x
   \]

2. Divide both sides by 2:
   \[
   6 \leq x
   \]
   or equivalently:
   \[
   x \geq 6
   \]

### Step 2: Solve \( 2x - 8 < 18 \)

1. Add 8 to both sides:
   \[
   2x < 26
   \]

2. Divide both sides by 2:
   \[
   x < 13
   \]

### Combine the results

The solution to the compound inequality is:
\[
6 \leq x < 13
\]

### Interval Notation

In interval notation, this is expressed as:
\[
[6, 13)
\]

### Answer

So, the exact answer in interval notation is:
\[
[6, 13)
\]

Would you like a further breakdown of any steps or have additional questions?

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Here are five related questions you might find helpful:
1. How do you solve compound inequalities involving "and" versus "or"?
2. What is the difference between interval notation and inequality notation?
3. How do you interpret open and closed brackets in interval notation?
4. How would the solution change if the inequality were reversed (e.g., \( 4 > 2x - 8 \))?
5. What are the steps for solving compound inequalities with three terms?

**Tip:** Always remember that solving compound inequalities typically involves separating them into two inequalities and solving each part individually.

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 compound inequalities and interval notation, suitable for students in Grades 8-10.

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