I have successfully opened the image. Let's work through the problem step-by-step using the provided values:

• $a = 9$
• $b = -3$
• $c = -2$
• $d = 7$

We'll evaluate each expression:

1. $a - cd$

Substitute the values: $9 - (-2 \cdot 7) = 9 + 14 = 23$

2. $2b^3 + c^2$

Substitute the values: $2(-3)^3 + (-2)^2 = 2(-27) + 4 = -54 + 4 = -50$

3. $\frac{a + d - c}{b}$

Substitute the values: $\frac{9 + 7 - (-2)}{-3} = \frac{9 + 7 + 2}{-3} = \frac{18}{-3} = -6$

4. $(a - b)^2 + d(a + c)$

Substitute the values: $(9 - (-3))^2 + 7(9 + (-2)) = (9 + 3)^2 + 7(9 - 2) = 12^2 + 7 \cdot 7 = 144 + 49 = 193$

5. $4c - (b - a)$

Substitute the values: $4(-2) - (-3 - 9) = -8 - (-12) = -8 + 12 = 4$

6. $\frac{a}{b} - 5a$

Substitute the values: $\frac{9}{-3} - 5(9) = -3 - 45 = -48$

7. $2bc + d(12 - 5)$

Substitute the values: $2(-3)(-2) + 7(12 - 5) = 12 + 7(7) = 12 + 49 = 61$

8. $b + 0.5[8 - (2c + a)]$

Substitute the values: [ -3 + 0.5[8 - (2(-2) + 9)] = -3 + 0.5[8 - (-4 + 9)] = -3 + 0.5[8 - 5] = -3 + 0.5(3) = -3 + 1.5 = -1.5 ]

Let me know if you'd like more detailed explanations or have any questions!

Here are 5 related questions:

1. How would the results change if $a$, $b$, $c$, and $d$ were fractions?
2. What happens to expression 6 if $b = 0$? How would you handle division by zero?
3. Can you generalize the result of expression 4 for any values of $a$, $b$, $c$, and $d$?
4. How do powers and negative signs affect the results in expressions 2 and 4?
5. What impact does the order of operations have in expression 8, especially with parentheses?

Tip: Always prioritize parentheses and exponents before multiplication and division to avoid common errors with negative numbers.