Sure, let's evaluate the expression [tex]\(4a - 2(a + b) + 1\)[/tex] step by step given that [tex]\(a = 2\)[/tex] and [tex]\(b = 4\)[/tex].
First, substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression:
[tex]\[ 4(2) - 2(2 + 4) + 1 \][/tex]
Next, perform the multiplication:
[tex]\[ 8 - 2(2 + 4) + 1 \][/tex]
Now, evaluate the expression inside the parentheses:
[tex]\[ 8 - 2(6) + 1 \][/tex]
Then, perform the multiplication:
[tex]\[ 8 - 12 + 1 \][/tex]
Finally, perform the additions and subtractions from left to right:
[tex]\[ 8 - 12 = -4 \][/tex]
[tex]\[ -4 + 1 = -3 \][/tex]
So, the value of the expression [tex]\(4a - 2(a + b) + 1\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = 4\)[/tex] is [tex]\(\boxed{-3}\)[/tex].
