To solve the equation $4x - 3y = -16$ for $x$, we isolate $x$ step by step:

Step-by-Step Solution:

1. Start with the given equation:
   $4x - 3y = -16$

2. Move $-3y$ to the right-hand side by adding $3y$ to both sides:
   $4x = 3y - 16$

3. Solve for $x$ by dividing through by 4:
   $x = \frac{3y}{4} - \frac{16}{4}$

4. Simplify the fractions:
   $x = \frac{3}{4}y - 4$

Final Answer:

The correct answer is:
$x = \frac{3}{4}y - 4$

This corresponds to the third option in the provided list.

Do you want me to explain any step further or provide examples? Let me know!

Related Questions:

1. How do you rearrange equations to solve for a specific variable?
2. How can you check if your solution for $x$ is correct?
3. What are the steps for solving linear equations with multiple variables?
4. How do you graph the equation $4x - 3y = -16$?
5. What are some real-world applications of solving for a variable in equations?

Tip:

Always ensure that each operation you perform (addition, subtraction, division) applies equally to both sides of the equation to maintain equality.