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Find the solution of the inequality [tex]-3n \ \textless \ 81[/tex].

A. [tex]n \ \textgreater \ -27[/tex]
B. [tex]n \ \textless \ 27[/tex]
C. [tex]n = -27[/tex]
D. [tex]n = 27[/tex]

Sagot :

GinnyAnswer
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]
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