To solve the given mathematical expression, we need to follow the order of operations, commonly remembered by the acronym BODMAS/PEMDAS (Brackets, Orders/Of, Division/Multiplication, Addition/Subtraction).

The expression is:

{7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + [9.2 × 4 - 2.46 of 3 + (36.3 ÷ 3 - 1.42 × 2)]}

Solving Mathematical Expression Step-by-Step

Step 1: Solve the innermost brackets (Parentheses)

First, we calculate the expression inside the innermost parentheses: (36.3 ÷ 3 - 1.42 × 2).

• Division: \(\frac{36.3}{3} = 12.1\)
• Multiplication: \(1.42 \times 2 = 2.84\)
• Subtraction: \(12.1 - 2.84 = 9.26\)

So, the innermost part evaluates to 9.26.

Step 2: Solve the expression within the square brackets

Next, we solve the expression inside the square brackets: [9.2 × 4 - 2.46 of 3 + (result from Step 1)].

• Multiplication: \(9.2 \times 4 = 37.44\)
• 'of' implies multiplication: \(2.46 \times 3 = 7.38\)
• Now substitute the result from Step 1: [37.44 - 7.38 + 9.26]
• Perform addition and subtraction from left to right:
  • \(37.44 - 7.38 = 30.06\)
  • \(30.06 + 9.26 = 39.32\)

The expression inside the square brackets evaluates to 39.32.

Step 3: Solve the remaining parts of the main expression

Now we evaluate the remaining multiplications, divisions, and then perform addition and subtraction for the main expression: {7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + (result from Step 2)}.

• Multiplication: \(7.88 \times 2 = 15.76\)
• Multiplication: \(2.4 \times 5 = 12.0\)
• Division: \(\frac{242.4}{4} = 60.6\)
• Substitute the result from Step 2: The expression becomes {15.76 + 12.0 - 60.6 + 39.32}

Step 4: Final Calculation

Perform the addition and subtraction from left to right:

• \(15.76 + 12.0 = 27.76\)
• \(27.76 - 60.6 = -32.84\)
• \(-32.84 + 39.32 = 6.48\)

The calculated value of the expression is 6.48.

Comparing this result with the given options, the closest value is 6.44 (Option 3). However, the provided correct answer is 5.84 (Option 2).