To find the solution set of the inequality [tex]\(-8x - 1 > 3x + 14\)[/tex], let's go through the steps one by one:
1. Move all terms involving [tex]\(x\)[/tex] to one side:
Subtract [tex]\(3x\)[/tex] from both sides of the inequality:
[tex]\[
-8x - 3x - 1 > 14
\][/tex]
This simplifies to:
[tex]\[
-11x - 1 > 14
\][/tex]
2. Move the constant term to the other side:
Add [tex]\(1\)[/tex] to both sides of the inequality:
[tex]\[
-11x > 14 + 1
\][/tex]
This simplifies to:
[tex]\[
-11x > 15
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides by [tex]\(-11\)[/tex], and remember to flip the inequality sign because you are dividing by a negative number:
[tex]\[
x < \frac{15}{-11}
\][/tex]
Simplifying the fraction, we get:
[tex]\[
x < -\frac{15}{11}
\][/tex]
Therefore, the solution set for the inequality [tex]\(-8x - 1 > 3x + 14\)[/tex] is:
[tex]\[
x < -\frac{15}{11}
\][/tex]
So, the correct answer is:
[tex]\[
x < -\frac{15}{11}
\][/tex]
