https://file.aiquickdraw.com/mathbot/file/1725592641394x60nbm7p.jpg

The problem in the image asks to solve the compound inequality:

\[
-25 > -2x - 5 > -29
\]

Let's solve this step by step.

### Step 1: Break down the inequality
We are dealing with a compound inequality:
\[
-25 > -2x - 5 > -29
\]
This means we need to solve both inequalities at the same time.

### Step 2: Solve the left side inequality
\[
-25 > -2x - 5
\]
Add 5 to both sides to eliminate the constant term on the right side:
\[
-25 + 5 > -2x
\]
\[
-20 > -2x
\]
Now, divide both sides by -2. Remember, when dividing by a negative number, we must reverse the inequality sign:
\[
\frac{-20}{-2} < \frac{-2x}{-2}
\]
\[
10 < x \quad \text{or} \quad x > 10
\]

### Step 3: Solve the right side inequality
\[
-2x - 5 > -29
\]
Add 5 to both sides:
\[
-2x > -24
\]
Now, divide both sides by -2, and again reverse the inequality sign:
\[
x < 12
\]

### Step 4: Combine the results
We now have two inequalities:
\[
10 < x < 12
\]
This is the solution to the compound inequality.

### Final Answer:
The solution is \( 10 < x < 12 \).

### Inequality Notation:
You can enter this in the "Inequality Notation" field as:
\[
(10, 12)
\]

### Graphing on the Number Line:
On the number line, graph an open interval between 10 and 12. Since the inequalities are strict (i.e., no "or equal to" involved), there should be open circles at 10 and 12, with the line between them shaded.

---

Would you like further details on graphing or solving compound inequalities?

Here are some related questions for deeper understanding:
1. How do we handle inequalities when dividing by negative numbers?
2. What happens if we switch the direction of the inequalities during the solution?
3. How can this inequality solution be checked by plugging in test values?
4. What if the inequality involved "greater than or equal to"?
5. How would the graph change if the inequality were \( x \leq 12 \)?

**Tip**: Always remember to reverse the inequality sign when multiplying or dividing by negative numbers!

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

Learn how to solve the compound inequality -25 > -2x - 5 > -29 step-by-step, including key algebraic concepts such as solving linear inequalities, reversing inequality signs, and graphing solutions on a number line. Suitable for Grades 8-10.

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