To evaluate the expression [tex]\(3 + 6 \cdot 4 - 16 + 2\)[/tex], we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
Here is the step-by-step solution:
1. Identify and perform the multiplication:
[tex]\[
3 + 6 \cdot 4 - 16 + 2
\][/tex]
Calculate [tex]\(6 \cdot 4\)[/tex]:
[tex]\[
6 \cdot 4 = 24
\][/tex]
Now the expression becomes:
[tex]\[
3 + 24 - 16 + 2
\][/tex]
2. Perform the addition and subtraction from left to right:
First, add [tex]\(3 + 24\)[/tex]:
[tex]\[
3 + 24 = 27
\][/tex]
Now the expression is:
[tex]\[
27 - 16 + 2
\][/tex]
Next, subtract [tex]\(27 - 16\)[/tex]:
[tex]\[
27 - 16 = 11
\][/tex]
Now the expression is:
[tex]\[
11 + 2
\][/tex]
Finally, add [tex]\(11 + 2\)[/tex]:
[tex]\[
11 + 2 = 13
\][/tex]
Therefore, the value of the expression [tex]\(3 + 6 \cdot 4 - 16 + 2\)[/tex] is [tex]\(\boxed{13}\)[/tex].
