Sure, let's break down this complex mathematical expression step-by-step:
### Step 1: Simplify the innermost expression
First, simplify [tex]\(5 + 3 - 2 - 7\)[/tex]:
[tex]\[
5 + 3 - 2 - 7 = -1
\][/tex]
### Step 2: Continue simplifying inside the nested parentheses
Next, use the result from Step 1 in the inner division and multiplication:
[tex]\[
3 \div 2 \times (-1)
\][/tex]
Perform the division first:
[tex]\[
3 \div 2 = 1.5
\][/tex]
Now multiply:
[tex]\[
1.5 \times (-1) = -1.5
\][/tex]
### Step 3: Proceed to the next level of the expression:
We now have:
[tex]\[
5 + (-1.5) = 3.5
\][/tex]
### Step 4: Continue simplifying the multiplication:
Next, multiply by 2:
[tex]\[
2 \times 3.5 = 7.0
\][/tex]
### Step 5: Next inner bracket division and multiplication:
Divide:
[tex]\[
2 \times 3 \div 7.0
\][/tex]
First, perform the multiplication:
[tex]\[
2 \times 3 = 6
\][/tex]
Then perform the division:
[tex]\[
6 \div 7.0 = 0.8571428571428571
\][/tex]
### Step 6: Next, multiply by 5:
[tex]\[
5 \times 0.8571428571428571 = 4.285714285714286
\][/tex]
### Step 7: Continue with addition and subtraction:
Add and subtract:
[tex]\[
4 + 4.285714285714286 - 4 = 4.285714285714285
\][/tex]
### Step 8: Finally, handle the external multiplication and addition:
First, resolve the innermost part:
[tex]\[
4 + 5 \times 4.285714285714285 + 15
\][/tex]
Multiply:
[tex]\[
5 \times 4.285714285714285 = 21.428571428571427
\][/tex]
Then add:
[tex]\[
4 + 21.428571428571427 + 15 = 40.42857142857143
\][/tex]
Finally, multiply by 3:
[tex]\[
3 \times 40.42857142857143 = 121.28571428571428
\][/tex]
Thus, the result of the given expression is:
[tex]\[
121.28571428571428
\][/tex]
