Sure, I'll guide you through solving the given expression step-by-step.
Here's the expression we need to solve:
[tex]$(7-5) \cdot [3-2-4 \div 2-3 \cdot (6-2-8 \div 4)]$[/tex]
### Step 1: Simplify the innermost parentheses
Let's start by simplifying the inner expression:
[tex]$(6-2-8 \div 4)$[/tex]
1. Perform the division inside the parentheses:
[tex]$8 \div 4 = 2$[/tex]
2. Substitute back into the expression:
[tex]$6-2-2$[/tex]
3. Perform the subtractions:
[tex]$6-2 = 4$[/tex]
[tex]$4-2 = 2$[/tex]
So, the result of the innermost parentheses is:
[tex]$(6-2-8 \div 4) = 2$[/tex]
### Step 2: Simplify the expression inside the brackets
Next, we'll handle the expression inside the brackets, substituting the result we just found:
[tex]$3-2-4 \div 2-3 \cdot 2$[/tex]
1. Perform the division:
[tex]$4 \div 2 = 2$[/tex]
2. Substitute back into the expression:
[tex]$3-2-2-3 \cdot 2$[/tex]
3. Perform the multiplication:
[tex]$3 \cdot 2 = 6$[/tex]
4. Substitute back into the expression:
[tex]$3-2-2-6$[/tex]
5. Perform the subtractions from left to right:
[tex]$3-2 = 1$[/tex]
[tex]$1-2 = -1$[/tex]
[tex]$-1-6 = -7$[/tex]
So, the result of the expression inside the brackets is:
[tex]$[3-2-4 \div 2-3 \cdot (6-2-8 \div 4)] = -7$[/tex]
### Step 3: Simplify the entire expression
Finally, we simplify the entire expression:
[tex]$(7-5) \cdot -7$[/tex]
1. Perform the subtraction:
[tex]$7-5 = 2$[/tex]
2. Multiply the result by -7:
[tex]$2 \cdot -7 = -14$[/tex]
So, the final result of the expression is:
[tex]$(7-5) \cdot [3-2-4 \div 2-3 \cdot (6-2-8 \div 4)] = -14$[/tex]
