To determine the value of the given expression [tex]\(\frac{|2a| - b}{3}\)[/tex] when [tex]\(a = 7\)[/tex] and [tex]\(b = -4\)[/tex], follow these steps:
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression.
[tex]\[
\frac{|2 \cdot 7| - (-4)}{3}
\][/tex]
2. Calculate [tex]\(2a\)[/tex], which is [tex]\(2 \cdot 7\)[/tex].
[tex]\[
2 \cdot 7 = 14
\][/tex]
3. Find the absolute value of [tex]\(14\)[/tex].
[tex]\[
|14| = 14
\][/tex]
4. Substitute the absolute value back into the expression.
[tex]\[
\frac{14 - (-4)}{3}
\][/tex]
5. Simplify the expression inside the numerator.
[tex]\[
14 - (-4) = 14 + 4 = 18
\][/tex]
6. Divide the numerator by 3.
[tex]\[
\frac{18}{3} = 6
\][/tex]
Thus, the value of the expression when [tex]\(a = 7\)[/tex] and [tex]\(b = -4\)[/tex] is [tex]\(\boxed{6}\)[/tex].
So, the correct answer is:
D. 6
