To solve the inequality [tex]\(-11x - 5 < 6\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Isolate the term with [tex]\(x\)[/tex]:
Start by getting rid of the constant term on the left side of the inequality. To do this, add 5 to both sides of the inequality:
[tex]\[
-11x - 5 + 5 < 6 + 5
\][/tex]
Simplifying this, you get:
[tex]\[
-11x < 11
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now, you need to isolate [tex]\(x\)[/tex]. To do this, divide both sides of the inequality by [tex]\(-11\)[/tex]. Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign:
[tex]\[
\frac{-11x}{-11} > \frac{11}{-11}
\][/tex]
Simplifying this, you get:
[tex]\[
x > -1
\][/tex]
So, the solution to the inequality [tex]\(-11x - 5 < 6\)[/tex] is:
[tex]\[
x > -1
\][/tex]
Among the given choices, the correct one is:
b. [tex]\(x > -1\)[/tex]
