Certainly! Let's tackle the expression step by step. The expression we need to simplify and solve is:
[tex]\[ -5 \cdot [6 \cdot (-2 + 3)] - (4 - 5) \cdot (-1) \][/tex]
### Step 1: Simplify Inside the Parentheses
First, we address the innermost parentheses:
[tex]\[ -2 + 3 \][/tex]
Simplifying this:
[tex]\[ -2 + 3 = 1 \][/tex]
### Step 2: Multiply by 6
Next, we multiply the result by 6:
[tex]\[ 6 \cdot 1 = 6 \][/tex]
### Step 3: Multiply by -5
Now, we take this result and multiply it by -5:
[tex]\[ -5 \cdot 6 = -30 \][/tex]
### Step 4: Simplify the Second Parentheses
Next, simplify the expression inside the second parentheses:
[tex]\[ 4 - 5 \][/tex]
This simplifies to:
[tex]\[ 4 - 5 = -1 \][/tex]
### Step 5: Multiply by -1
Now we multiply the result by -1:
[tex]\[ -1 \cdot -1 = 1 \][/tex]
### Step 6: Combine the Results
Finally, we need to combine the results from steps 3 and 5:
[tex]\[ -30 - 1 \][/tex]
This simplifies to:
[tex]\[ -30 - 1 = -31 \][/tex]
### Final Answer
Therefore, the simplified and final result is:
[tex]\[ -31 \][/tex]
