1.      Evaluate each expression if 𝑎 = 4, 𝑏 = −2, and 𝑐 = −3 **using the order of operations**. **[7 marks]**
**** 
**** 
(a)

−(𝑎+2)2− 4𝑐 2−𝑏
 
 
(b)

6𝑎− 3𝑏3
 

−5[−7−𝑐]

Let's evaluate each expression step by step using the given values \( a = 4 \), \( b = -2 \), and \( c = -3 \). We'll carefully follow the order of operations (PEMDAS).

### (a) Expression: \( -\frac{(a + 2)2 - 4c}{2 - b} \)

1. **Substitute the values**:
   \[
   -\frac{(4 + 2)2 - 4(-3)}{2 - (-2)}
   \]

2. **Simplify inside the parentheses**:
   \[
   -\frac{(6)2 - 4(-3)}{2 + 2}
   \]

3. **Multiply inside the numerator**:
   \[
   -\frac{12 + 12}{4} = -\frac{24}{4}
   \]

4. **Simplify the division**:
   \[
   -6
   \]

So, the value of expression (a) is **-6**.

### (b) Expression: \( 6a - \frac{3b}{3} - 5[-7 - c] \)

1. **Substitute the values**:
   \[
   6(4) - \frac{3(-2)}{3} - 5[-7 - (-3)]
   \]

2. **Multiply and simplify**:
   \[
   24 - \frac{-6}{3} - 5[-7 + 3]
   \]

3. **Simplify inside the division and brackets**:
   \[
   24 + 2 - 5[-4]
   \]

4. **Multiply inside the brackets**:
   \[
   24 + 2 + 20 = 46
   \]

So, the value of expression (b) is **46**.

### Final Answers:
1. **(a)**: \(-6\)
2. **(b)**: \(46\)

Would you like more details on these steps or have any further questions?

Here are 5 related questions for practice:
1. Evaluate \( \frac{(a - b)c}{a - 2} \) using \( a = 4 \), \( b = -2 \), and \( c = -3 \).
2. What is the value of \( 4a - \frac{b}{c} + 2c \) if \( a = 4 \), \( b = -2 \), and \( c = -3 \)?
3. Simplify \( 3a + \frac{b^2 - c^2}{a} \) using \( a = 4 \), \( b = -2 \), and \( c = -3 \).
4. Calculate \( 7b + \frac{c}{a} - b^2 \) when \( b = -2 \) and \( c = -3 \).
5. Find the result of \( \frac{-2a + 3c}{b + 1} \) given \( a = 4 \), \( b = -2 \), and \( c = -3 \).

**Tip:** When dealing with complex fractions, simplify the numerator and denominator separately before dividing.

Learn how to evaluate mathematical expressions using the order of operations with detailed step-by-step solutions. This problem covers substitution, simplification, and the application of PEMDAS. Suitable for students in Grades 9-12.

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