To solve the problem, we want to determine the value of [tex]\((q - p)(6)\)[/tex] given the functions [tex]\(p(x) = 5x + 30\)[/tex] and [tex]\(q(x) = 11x - 24\)[/tex].
Here's the step-by-step process:
1. Evaluate [tex]\(p(x)\)[/tex] at [tex]\(x = 6\)[/tex]:
[tex]\[
p(6) = 5(6) + 30 = 30 + 30 = 60
\][/tex]
2. Evaluate [tex]\(q(x)\)[/tex] at [tex]\(x = 6\)[/tex]:
[tex]\[
q(6) = 11(6) - 24 = 66 - 24 = 42
\][/tex]
3. Calculate [tex]\((q - p)(6)\)[/tex]:
[tex]\[
(q - p)(6) = q(6) - p(6)
\][/tex]
Substituting the evaluated values from steps 1 and 2:
[tex]\[
(q - p)(6) = 42 - 60 = -18
\][/tex]
Thus, the value of [tex]\((q - p)(6)\)[/tex] is [tex]\(-18\)[/tex]. Therefore, the correct answer is:
D. -18
