Sure, let's solve the given expression step by step.
We are provided with the expression:
[tex]\[
\frac{|2a| - b}{3}
\][/tex]
and the values [tex]\( a = 7 \)[/tex] and [tex]\( b = -4 \)[/tex].
First, we need to substitute [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the expression.
1. Calculate [tex]\( 2a \)[/tex]:
[tex]\[
2a = 2 \times 7 = 14
\][/tex]
2. Calculate the absolute value of [tex]\( 2a \)[/tex]:
[tex]\[
|2a| = |14| = 14
\][/tex]
3. Substitute [tex]\( |2a| \)[/tex] and [tex]\( b \)[/tex] into the expression:
[tex]\[
\frac{|2a| - b}{3} = \frac{14 - (-4)}{3}
\][/tex]
4. Simplify inside the numerator:
[tex]\[
14 - (-4) = 14 + 4 = 18
\][/tex]
5. Divide 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]\[
6
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{6}
\][/tex]
This corresponds to option D.
