Of course! Let's break down the given complex mathematical expression step by step. The expression we need to evaluate is:
[tex]\[ 84 - \left[26 - \left\{12 \div 3 \times 2\right\}\right] \times 43 \times 2 \][/tex]
### Step 1: Evaluate the innermost brackets
First, we evaluate the innermost expression within the curly braces:
[tex]\[ 12 \div 3 \times 2 \][/tex]
By following the order of operations (PEMDAS/BODMAS), where we perform division and multiplication from left to right:
[tex]\[ \frac{12}{3} = 4 \][/tex]
[tex]\[ 4 \times 2 = 8 \][/tex]
Thus:
[tex]\[ \left\{12 \div 3 \times 2\right\} = 8 \][/tex]
### Step 2: Substitute back into the expression
We substitute [tex]\( 8 \)[/tex] back into the expression within the square brackets:
[tex]\[ 26 - 8 \][/tex]
### Step 3: Perform the subtraction
Perform the subtraction inside the square brackets:
[tex]\[ 26 - 8 = 18 \][/tex]
### Step 4: Multiply the result by 43 and then by 2
Next, we need to multiply [tex]\( 18 \)[/tex] by [tex]\( 43 \)[/tex] and then by [tex]\( 2 \)[/tex]:
[tex]\[ 18 \times 43 \times 2 \][/tex]
First, calculate [tex]\( 18 \times 43 \)[/tex]:
[tex]\[ 18 \times 43 = 774 \][/tex]
Then multiply the result by [tex]\( 2 \)[/tex]:
[tex]\[ 774 \times 2 = 1548 \][/tex]
### Step 5: Substitute back into the original expression
We now substitute [tex]\( 1548 \)[/tex] back into the original expression at the position we subtracted it from [tex]\( 84 \)[/tex]:
[tex]\[ 84 - 1548 \][/tex]
### Step 6: Perform the final subtraction
Finally, perform the subtraction:
[tex]\[ 84 - 1548 = -1464 \][/tex]
### Final result
The value of the given expression is:
[tex]\[ -1464 \][/tex]
