https://file.aiquickdraw.com/mathbot/file/17261017546275kp7d3xp.jpg

Let's solve the equation step-by-step:

Given:
\[
-7x - 16 = 2x + 11
\]

### Step 1: Move all terms involving \(x\) to one side of the equation
Add \(7x\) to both sides:
\[
-16 = 9x + 11
\]

### Step 2: Move constant terms to the other side
Subtract 11 from both sides:
\[
-16 - 11 = 9x
\]
\[
-27 = 9x
\]

### Step 3: Solve for \(x\)
Divide both sides by 9:
\[
x = \frac{-27}{9}
\]
\[
x = -3
\]

Thus, the correct solution is:
\[
x = -3
\]

The answer is **A. \(x = -3\)**.

Would you like more details on any step? Here are five related questions to help deepen your understanding:

1. What is the general process for solving linear equations with variables on both sides?
2. Why is it important to move terms involving \(x\) to one side of the equation first?
3. How do you check if the solution to a linear equation is correct?
4. What are examples of equations where the solution is all real numbers (option B)?
5. Can you explain scenarios where an equation has no solution (option C)?

**Tip:** When solving equations, always try to simplify both sides step by step to avoid errors!

Learn how to solve the linear equation -7x - 16 = 2x + 11 step-by-step. This problem demonstrates key concepts in algebra and linear equations, suitable for students in Grades 7-9.

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