Let's solve the inequality step-by-step.
We start with the inequality:
[tex]\[
-122 < -3(-2 - 8x) - 8x
\][/tex]
First, we need to distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[
-3(-2 - 8x) = -3 \cdot (-2) - 3 \cdot (8x) = 6 + 24x
\][/tex]
So the inequality becomes:
[tex]\[
-122 < 6 + 24x - 8x
\][/tex]
Next, we combine like terms:
[tex]\[
24x - 8x = 16x
\][/tex]
So the inequality is now:
[tex]\[
-122 < 6 + 16x
\][/tex]
Our next step is to isolate the term containing [tex]\(x\)[/tex]. We do this by subtracting 6 from both sides:
[tex]\[
-122 - 6 < 16x \implies -128 < 16x
\][/tex]
Now, we divide both sides by 16 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{-128}{16} < x \implies -8 < x
\][/tex]
This can also be written as:
[tex]\[
x > -8
\][/tex]
Thus, the solution to the inequality [tex]\( -122 < -3(-2 - 8x) - 8x \)[/tex] is:
[tex]\[
\boxed{x > -8}
\][/tex]
So, the correct answer is:
C. [tex]\( x > -8 \)[/tex]
