Let's solve this step by step based on the questions shown in your uploaded image.

Question 1: Distribute the $-2$

The inequality starts as: $-2(x + 6) < -7$ Distribute $-2$ to the terms inside the parentheses: $-2x - 12 < -7$ The correct option for this step is B: $-2x - 12$.

Question 2: When dividing or multiplying by a negative, what happens to the inequality?

When dividing or multiplying both sides of an inequality by a negative number, the inequality flips (reverses direction). Therefore, the answer is A: flip.

Question 3: Solve for $x$

From the distributed inequality: $-2x - 12 < -7$

1. Add 12 to both sides: $-2x < 5$

2. Divide both sides by $-2$. Since we are dividing by a negative, flip the inequality: $x > -\frac{5}{2}$

The solution is: $x > -\frac{5}{2}$

Thus, the answer for this step is A: $-5/2$ (but note this should be written as $x > -5/2$, not $x <$).

Let me know if you’d like further clarifications or details!

Expanding Questions:

1. What happens to inequalities when you multiply or divide by zero?
2. How can you verify solutions to inequalities on a number line?
3. What are common mistakes when solving multistep inequalities?
4. How does solving inequalities differ from solving equations?
5. Why does the inequality sign flip only with negative division or multiplication?

Tip: Always double-check your inequality direction after dividing by a negative to avoid mistakes!