https://file.aiquickdraw.com/mathbot/file/17261065554618r8zxgrd.jpg

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!

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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.

Evaluate each expression for a = 9, b = -3, c = -2, d = 7. Show your work.

Solve and evaluate various algebraic expressions using substitution for a = 9, b = -3, c = -2, and d = 7. This includes key algebraic concepts like powers, fractions, and order of operations. Detailed step-by-step solutions provided. Suitable for Grades 7-10.

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