To solve the inequality $-3(7x + 11) < 2(2x - 4)$, we will follow these steps:

Step 1: Expand both sides of the inequality

Distribute the numbers outside the parentheses on both sides:

$-3(7x + 11) = -21x - 33$ $2(2x - 4) = 4x - 8$

So the inequality becomes: $-21x - 33 < 4x - 8$

Step 2: Move the variable terms to one side

Add $21x$ to both sides to move all terms with $x$ to the right: $-33 < 25x - 8$

Step 3: Move the constant terms to the other side

Add 8 to both sides: $-33 + 8 < 25x$ $-25 < 25x$

Step 4: Solve for $x$

Now, divide both sides by 25: $x > -1$

Final Answer:

The solution set is $x > -1$, which corresponds to option D.

Would you like more details on any step? Here are 5 related questions:

1. How would the solution change if the inequality were $>$ instead of $<$?
2. What happens when the coefficient of $x$ is negative?
3. How do you solve inequalities involving fractions?
4. What is the significance of switching the inequality sign when multiplying or dividing by a negative number?
5. How can inequalities be graphed on a number line?

Tip: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.