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Let's solve the inequality step by step:

The inequality given is:
\[
-2x - 6 > 3x + 14
\]

### Step 1: Move the \(3x\) term to the left side by subtracting \(3x\) from both sides:
\[
-2x - 3x - 6 > 14
\]
\[
-5x - 6 > 14
\]

### Step 2: Move the \(-6\) to the right side by adding 6 to both sides:
\[
-5x > 14 + 6
\]
\[
-5x > 20
\]

### Step 3: Solve for \(x\) by dividing both sides by \(-5\). **Remember that when you divide or multiply an inequality by a negative number, the direction of the inequality sign must be reversed**:
\[
x < \frac{20}{-5}
\]
\[
x < -4
\]

The correct answer is:
\[
\text{B. } x < -4
\]

Would you like more details or have any other questions?

Here are five related questions:
1. How do you solve inequalities that involve multiplying or dividing by negative numbers?
2. What is the difference between solving equations and solving inequalities?
3. How can you represent the solution of an inequality on a number line?
4. What happens if you accidentally forget to flip the inequality sign when dividing by a negative number?
5. How do you solve compound inequalities?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Master the technique of solving the linear inequality -2x - 6 > 3x + 14 with a comprehensive step-by-step guide. This problem is ideal for students in Grades 8-10 and covers important algebraic concepts like inequality manipulation and understanding the reversal of inequality signs when dividing by a negative number.

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