To simplify [tex]\(2 + 3 - 4 + (5 \times 4)\)[/tex], we'll follow the order of operations, which can be remembered by the acronym PEMDAS:
Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Following these steps:
1. Parentheses first: We have [tex]\(5 \times 4\)[/tex] inside the parentheses.
[tex]\[
5 \times 4 = 20
\][/tex]
Now our expression becomes:
[tex]\[
2 + 3 - 4 + 20
\][/tex]
2. Addition and Subtraction (from left to right): Let's process the expression from left to right.
First, we perform the addition:
[tex]\[
2 + 3 = 5
\][/tex]
Now the expression is:
[tex]\[
5 - 4 + 20
\][/tex]
Next, perform the subtraction:
[tex]\[
5 - 4 = 1
\][/tex]
Now the expression is:
[tex]\[
1 + 20
\][/tex]
Finally, perform the last addition:
[tex]\[
1 + 20 = 21
\][/tex]
The simplified value of the expression [tex]\(2 + 3 - 4 + (5 \times 4)\)[/tex] is [tex]\(\boxed{21}\)[/tex]. Thus, the correct answer is:
A. 21
