The problem is to evaluate the following expression: $5[6.4 - \{5.5 + 2(2.8 + 3.6 - 2.1)\}] \div 4$. We need to follow the order of operations (PEMDAS/BODMAS).

1. Problem Description

The problem is to evaluate the following expression: $5[6.4 - \{5.5 + 2(2.8 + 3.6 - 2.1)\}] \div 4$. We need to follow the order of operations (PEMDAS/BODMAS).

2. Solution Steps

First, we solve the innermost parentheses:

$2.8 + 3.6 - 2.1 = 6.4 - 2.1 = 4.3$

Now, we substitute this result back into the expression:

$5[6.4 - \{5.5 + 2(4.3)\}] \div 4$

Next, we perform the multiplication within the curly braces:

$2(4.3) = 8.6$

Substitute this result back into the expression:

$5[6.4 - \{5.5 + 8.6\}] \div 4$

Now, we solve the addition within the curly braces:

$5.5 + 8.6 = 14.1$

Substitute this result back into the expression:

$5[6.4 - 14.1] \div 4$

Next, we perform the subtraction within the square brackets:

$6.4 - 14.1 = -7.7$

Substitute this result back into the expression:

$5[-7.7] \div 4$

Now, we perform the multiplication:

$5(-7.7) = -38.5$

Substitute this result back into the expression:

$-38.5 \div 4$

Finally, we perform the division:

$-38.5 \div 4 = -9.625$

3. Final Answer

-9.625