Let's go through the two problems in the image step by step.

First Problem:

Expression: $-\frac{2}{3}(6x - 9)$

Step 1: Distribute $-\frac{2}{3}$ to each term inside the parentheses.

• Distribute to $6x$: $-\frac{2}{3} \times 6x = -4x$
• Distribute to $-9$: $-\frac{2}{3} \times (-9) = 6$

Final Expression: $-4x + 6$

Second Problem:

Expression: $(4 - \frac{5}{2}x)6$

Step 1: Distribute $6$ to each term inside the parentheses.

• Distribute to $4$: $6 \times 4 = 24$
• Distribute to $-\frac{5}{2}x$: $6 \times -\frac{5}{2}x = -15x$

Final Expression: $24 - 15x$

Would you like further explanation on any step? Here are five related questions that could help reinforce understanding:

1. What is the Distributive Property, and why is it important in algebra?
2. How do you handle negative signs when distributing in expressions?
3. What happens if there are multiple variables inside the parentheses?
4. How can you apply the Distributive Property to more complex expressions involving multiple terms?
5. Can you explain how to factor out a common term using the reverse of the Distributive Property?

Tip: Always be careful with signs when distributing, especially with negative coefficients.