To find the solution of the inequality [tex]\(-3n < 81\)[/tex], we need to isolate [tex]\(n\)[/tex]. Let's walk through the steps to solve this inequality:
1. Start with the given inequality:
[tex]\[
-3n < 81
\][/tex]
2. Isolate [tex]\(n\)[/tex] by dividing both sides of the inequality by [tex]\(-3\)[/tex]:
- It is important to remember that when you divide an inequality by a negative number, the direction of the inequality sign reverses.
So, dividing both sides by [tex]\(-3\)[/tex]:
[tex]\[
n > \frac{81}{-3}
\][/tex]
3. Simplify the right side:
[tex]\[
n > -27
\][/tex]
Thus, the solution to the inequality [tex]\(-3n < 81\)[/tex] is [tex]\(n > -27\)[/tex].
Now, let’s look at the given choices:
- A. [tex]\(n > -27\)[/tex]
- B. [tex]\(n < 27\)[/tex]
- C. [tex]\(n = -27\)[/tex]
- D. [tex]\(n = 27\)[/tex]
The correct answer is:
A. [tex]\(n > -27\)[/tex]
