Sure, let's proceed step by step to simplify the given expression. The expression is:
[tex]\[ 35 - 2 + 3 \cdot \pi - 2 = 3 \][/tex]
### Step-by-Step Solution:
1. Identify all operations: We need to handle subtraction, addition, and multiplication.
2. Perform the multiplication first (according to the order of operations): Calculate [tex]\(3 \cdot \pi\)[/tex].
Since [tex]\(\pi\)[/tex] approximately equals 3.14159:
[tex]\[
3 \cdot \pi \approx 3 \cdot 3.14159 = 9.42477
\][/tex]
Now, substitute this value back into the expression:
[tex]\[
35 - 2 + 9.42477 - 2 = 3
\][/tex]
3. Perform the subtractions and addition from left to right:
- First, compute [tex]\(35 - 2\)[/tex]:
[tex]\[
35 - 2 = 33
\][/tex]
- Next, add the intermediate result to 9.42477:
[tex]\[
33 + 9.42477 = 42.42477
\][/tex]
- Finally, subtract 2:
[tex]\[
42.42477 - 2 = 40.42477
\][/tex]
So, the left-hand side (LHS) of the equation simplifies to:
[tex]\[
40.42477
\][/tex]
4. Compare the two sides:
The left-hand side (LHS) is now 40.42477, while the right-hand side (RHS) is 3.
It's clear that:
[tex]\[
40.42477 \neq 3
\][/tex]
### Conclusion:
- The left-hand side (LHS) of the simplified expression [tex]\(35 - 2 + 3 \cdot \pi - 2\)[/tex] is approximately 40.42477.
- The right-hand side (RHS) is 3.
- Since 40.42477 does not equal 3, the original equation does not hold true.
Hence, the final simplified value of the expression [tex]\( 35 - 2 + 3 \cdot \pi - 2 \)[/tex] is approximately 40.42477.
