To find the value of the expression [tex]\(\frac{|2 a| - b}{3}\)[/tex] for [tex]\(a = 7\)[/tex] and [tex]\(b = -4\)[/tex], follow these steps:
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- [tex]\(a = 7\)[/tex]
- [tex]\(b = -4\)[/tex]
2. Calculate the inside expressions:
- Calculate [tex]\(2a\)[/tex]:
[tex]\[
2 \cdot 7 = 14
\][/tex]
- Calculate the absolute value of [tex]\(2a\)[/tex]:
[tex]\[
|2 \cdot 7| = |14| = 14
\][/tex]
- Calculate [tex]\(-b\)[/tex]:
[tex]\[
-(-4) = 4
\][/tex]
3. Substitute these results into the numerator [tex]\(|2a| - b\)[/tex]:
[tex]\[
14 + 4 = 18
\][/tex]
4. Divide the numerator by 3 to find the value of the expression:
[tex]\[
\frac{18}{3} = 6
\][/tex]
Therefore, the value of the expression is 6.
So, the correct answer is:
[tex]\[ \boxed{6} \][/tex]
