The inequality provided in the image is:

$-(3x + 3) - 2x > -4(x - 2) - 2$

Step-by-step solution:

1. Expand both sides:

   • On the left:
     $-(3x + 3) = -3x - 3$ So the left-hand side becomes:
     $-3x - 3 - 2x = -5x - 3$
   • On the right:
     $-4(x - 2) = -4x + 8$ So the right-hand side becomes:
     $-4x + 8 - 2 = -4x + 6$

2. Rewrite the inequality: $-5x - 3 > -4x + 6$

3. Add $4x$ to both sides to move $x$ terms to one side: $-5x + 4x - 3 > 6$ Simplifying: $-x - 3 > 6$

4. Add 3 to both sides: $-x > 9$

5. Multiply both sides by -1 (remember to flip the inequality sign): $x < -9$

Final solution:

The inequality is $x < -9$. Therefore, the correct answer is:

$\boxed{x < -9}$

Would you like further details on any part of the process or additional related questions?

Related Questions:

1. How do you solve linear inequalities with fractions?
2. What happens when you multiply or divide an inequality by a negative number?
3. How do you check if your solution to an inequality is correct?
4. What are the different ways to express inequality solutions (interval notation, graphing, etc.)?
5. How would the solution change if the inequality symbol were $\geq$ instead of $>$?

Tip: Always remember to flip the inequality sign when multiplying or dividing by a negative number!