To solve the inequality [tex]\(-122 < -3(-2 - 8x) - 8x\)[/tex], let's go through the steps methodically:
1. Distribute and Simplify the Expression:
Begin by distributing the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[
-122 < -3(-2 - 8x) - 8x
\][/tex]
[tex]\[
-122 < (-3 \cdot -2) + (-3 \cdot -8x) - 8x
\][/tex]
This gives us:
[tex]\[
-122 < 6 + 24x - 8x
\][/tex]
2. Combine Like Terms:
Now combine the terms involving [tex]\(x\)[/tex]:
[tex]\[
-122 < 6 + 16x
\][/tex]
3. Isolate the Variable Term:
Subtract 6 from both sides to begin isolating the term with [tex]\(x\)[/tex]:
[tex]\[
-128 < 16x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides by 16 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{-128}{16} < x
\][/tex]
[tex]\[
-8 < x
\][/tex]
This inequality tells us that [tex]\(x\)[/tex] must be greater than [tex]\(-8\)[/tex].
So the solution to the inequality [tex]\(-122 < -3(-2 - 8x) - 8x\)[/tex] is:
[tex]\[
x > -8
\][/tex]
The best answer from the given options is:
B. [tex]\( x > -8 \)[/tex]
