Let's evaluate the expression [tex]\(-2\left|x^2 - 15\right| - 4\)[/tex] when [tex]\(x = -3\)[/tex].
1. Substitute [tex]\(x = -3\)[/tex] into the expression inside the absolute value:
[tex]\[
x^2 - 15
\][/tex]
[tex]\[
(-3)^2 - 15
\][/tex]
2. Calculate [tex]\((-3)^2 - 15\)[/tex]:
[tex]\[
9 - 15 = -6
\][/tex]
So, [tex]\((x^2 - 15)\)[/tex] evaluates to [tex]\(-6\)[/tex].
3. Find the absolute value of [tex]\(-6\)[/tex]:
[tex]\[
\left|-6\right| = 6
\][/tex]
4. Substitute the absolute value back into the original expression:
[tex]\[
-2\left|x^2 - 15\right| - 4
\][/tex]
[tex]\[
-2(6) - 4
\][/tex]
5. Calculate [tex]\(-2(6) - 4\)[/tex]:
[tex]\[
-12 - 4 = -16
\][/tex]
Therefore, the value of the expression when [tex]\(x = -3\)[/tex] is [tex]\(-16\)[/tex]. The correct answer is:
[tex]\[
\boxed{-16}
\][/tex]
