Let's solve the expression step by step:
[tex]\[ -5 + \frac{5}{5} \cdot \left[ -4 + 3 \left( -2 + \frac{5}{-4} \right) \right] - 4 - 8 - 2 \][/tex]
1. Evaluate the innermost parenthesis:
[tex]\[ \frac{5}{-4} = -1.25 \][/tex]
So, the expression inside the inner parentheses becomes:
[tex]\[ -2 + (-1.25) = -3.25 \][/tex]
2. Multiply 3 by the result of the inner expression:
[tex]\[ 3 \cdot (-3.25) = -9.75 \][/tex]
3. Evaluate the expression inside the brackets:
[tex]\[ -4 + (-9.75) = -13.75 \][/tex]
4. Evaluate the division and multiplication:
[tex]\[ \frac{5}{5} = 1 \][/tex]
Then,
[tex]\[ 1 \cdot (-13.75) = -13.75 \][/tex]
5. Combine all parts of the expression:
Now, substitute back into the original expression and simplify:
[tex]\[ -5 + (-13.75) - 4 - 8 - 2 \][/tex]
6. Simplify the expression step-by-step:
Combine the terms:
[tex]\[ -5 - 13.75 = -18.75 \][/tex]
[tex]\[ -18.75 - 4 = -22.75 \][/tex]
[tex]\[ -22.75 - 8 = -30.75 \][/tex]
[tex]\[ -30.75 - 2 = -32.75 \][/tex]
So, the final result of the given expression is:
[tex]\[ -32.75 \][/tex]
