To solve the inequality [tex]\(-8x - 1 > 3x + 14\)[/tex] step by step, we can follow these steps:
1. Move all variable terms to one side of the inequality.
To isolate the terms involving [tex]\(x\)[/tex], let's add [tex]\(8x\)[/tex] to both sides of the inequality:
[tex]\[
-8x - 1 + 8x > 3x + 14 + 8x
\][/tex]
Simplifying this, we get:
[tex]\[
-1 > 11x + 14
\][/tex]
2. Move all constant terms to the other side of the inequality.
To further isolate [tex]\(x\)[/tex], let's subtract 14 from both sides of the inequality:
[tex]\[
-1 - 14 > 11x
\][/tex]
Simplifying this, we get:
[tex]\[
-15 > 11x
\][/tex]
3. Isolate [tex]\(x\)[/tex] by dividing both sides by the coefficient of [tex]\(x\)[/tex].
We need to divide both sides by 11 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{-15}{11} > x
\][/tex]
This means:
[tex]\[
x < \frac{-15}{11}
\][/tex]
Thus, the solution set for the inequality [tex]\(-8x - 1 > 3x + 14\)[/tex] is:
[tex]\[
x < -\frac{15}{11}
\][/tex]
Among the given choices, the correct answer is:
[tex]\[
x < -\frac{15}{11}
\][/tex]
