Let's solve the given expression step-by-step to find its value when [tex]\(a = 7\)[/tex] and [tex]\(b = -4\)[/tex]:
The expression is:
[tex]\[
\frac{|2a| - b}{3}
\][/tex]
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
a = 7
\][/tex]
[tex]\[
b = -4
\][/tex]
2. Calculate [tex]\(2a\)[/tex]:
[tex]\[
2a = 2 \times 7 = 14
\][/tex]
3. Calculate the absolute value [tex]\(|2a|\)[/tex]:
[tex]\[
|2a| = |14| = 14
\][/tex]
4. Substitute [tex]\(|2a|\)[/tex] and [tex]\(b\)[/tex] into the expression:
[tex]\[
\frac{|2a| - b}{3} = \frac{14 - (-4)}{3}
\][/tex]
5. Simplify the expression by handling the double negative:
[tex]\[
14 - (-4) = 14 + 4 = 18
\][/tex]
6. Divide the result by 3:
[tex]\[
\frac{18}{3} = 6
\][/tex]
Therefore, the value of the expression when [tex]\(a = 7\)[/tex] and [tex]\(b = -4\)[/tex] is:
[tex]\[
\boxed{6}
\][/tex]
The correct answer is:
D. 6
