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To solve the inequality \(-25 > -2x - 5 > -29\), we'll break it down into two parts:

1. **First Inequality: \(-25 > -2x - 5\)**

   \[
   -25 > -2x - 5
   \]

   Add 5 to both sides:

   \[
   -20 > -2x
   \]

   Now, divide by -2. Remember to reverse the inequality sign when dividing by a negative number:

   \[
   10 < x
   \]

   So, this inequality becomes:

   \[
   x > 10
   \]

2. **Second Inequality: \(-2x - 5 > -29\)**

   \[
   -2x - 5 > -29
   \]

   Add 5 to both sides:

   \[
   -2x > -24
   \]

   Divide by -2 (again, reversing the inequality sign):

   \[
   x < 12
   \]

   So, this inequality becomes:

   \[
   x < 12
   \]

3. **Combining Both Inequalities:**

   Now, combining both solutions:

   \[
   10 < x < 12
   \]

4. **Graphing on the Number Line:**

   On the number line, the interval \( (10, 12) \) will be represented with an open circle at both 10 and 12, indicating that these endpoints are not included in the solution.

5. **Final Answer:**

   - Inequality Notation: \( 10 < x < 12 \)
   - On the number line, place open circles at 10 and 12 and shade the region in between.

Would you like a more detailed explanation or have any further questions?

### 5 Related Questions:
1. How do you solve compound inequalities with more than two inequalities?
2. What happens if you forget to reverse the inequality sign when multiplying or dividing by a negative number?
3. How do you solve and graph inequalities involving absolute values?
4. What is the difference between strict inequalities and inclusive inequalities on a graph?
5. How do you represent solutions to inequalities in interval notation?

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

Solve for x and graph the solution on the number line: -25 > -2x - 5 > -29.

Learn how to solve and graph the compound inequality -25 > -2x - 5 > -29. This problem covers key algebraic concepts, including reversing the inequality when dividing by a negative. Suitable for students in Grades 8-10.

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