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The given inequality is:

\[
-18 < -2x - 7 < 0
\]

This is a compound inequality, which means we need to solve for \(x\) in the middle portion by handling both inequalities simultaneously.

### Step-by-step solution:

1. Start with the inequality: 
   \[
   -18 < -2x - 7 < 0
   \]

2. Solve the left part of the inequality:
   \[
   -18 < -2x - 7
   \]

   Add 7 to both sides:
   \[
   -18 + 7 < -2x
   \]
   Simplifying:
   \[
   -11 < -2x
   \]

   Divide both sides by \(-2\) (and reverse the inequality sign since dividing by a negative number):
   \[
   \frac{-11}{-2} > x \quad \text{or} \quad x < \frac{11}{2}
   \]

   Simplifying:
   \[
   x < 5.5
   \]

3. Now, solve the right part of the inequality:
   \[
   -2x - 7 < 0
   \]

   Add 7 to both sides:
   \[
   -2x < 7
   \]

   Divide both sides by \(-2\) (again, reverse the inequality sign):
   \[
   x > -\frac{7}{2} \quad \text{or} \quad x > -3.5
   \]

4. Combining the two results, we have:
   \[
   -3.5 < x < 5.5
   \]

### Final Answer:
The solution to the inequality is:
\[
x \in (-3.5, 5.5)
\]

Would you like further clarification on any of these steps?

### Related Questions:
1. How do you solve a compound inequality with more complex terms?
2. What happens to inequality signs when dividing by negative numbers?
3. Can we represent the solution graphically on a number line?
4. How does solving inequalities differ from solving equalities?
5. What is the difference between strict and non-strict inequalities?

### Tip:
Always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Explore how to solve the compound inequality -18 < -2x - 7 < 0 with a detailed step-by-step solution. This problem involves key algebraic concepts such as solving compound inequalities and understanding the impact of dividing by negative numbers. Suitable for students in Grades 7-9.

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