To solve the compound inequality \(3 > -x - 3 > -5\), we will break it down into two separate inequalities and solve them step by step.

### Step 1: Break the compound inequality into two parts

1. \(3 > -x - 3\)
2. \(-x - 3 > -5\)

### Step 2: Solve each inequality

**Inequality 1:** \(3 > -x - 3\)

Add \(3\) to both sides:
\[
3 + 3 > -x - 3 + 3
\]
\[
6 > -x
\]

Multiply both sides by \(-1\) and reverse the inequality sign:
\[
-x < 6 \implies x > -6
\]

**Inequality 2:** \(-x - 3 > -5\)

Add \(3\) to both sides:
\[
-x - 3 + 3 > -5 + 3
\]
\[
-x > -2
\]

Multiply both sides by \(-1\) and reverse the inequality sign:
\[
x < 2
\]

### Step 3: Combine the solutions

The solutions for \(x\) from both inequalities are:
\[
x > -6 \quad \text{and} \quad x < 2
\]

### Step 4: Write the final solution

The solution for the compound inequality is:
\[
-6 < x < 2
\]

So, \(x\) is any value between \(-6\) and \(2\), not including \(-6\) and \(2\).

Would you like more details or have any questions about the solution?

### Here are some related questions you might consider:
1. How would the solution change if the inequality was \(3 \geq -x - 3 \geq -5\)?
2. What are the steps to solve \(4 \leq -2x + 1 < 10\)?
3. How can we represent the solution \(-6 < x < 2\) on a number line?
4. What are compound inequalities, and how do they differ from simple inequalities?
5. How do we solve compound inequalities that involve fractions?

**Tip:** When solving inequalities, remember to flip the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the compound inequality 3 > -x - 3 > -5 with a detailed step-by-step solution. This problem covers key concepts in inequalities and is suitable for high school students.

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