Question

You found that n = -8 is the boundary point. That is the point that separates numbers that are solutions from numbers that are not solutions. What is the solution to the inequality?

n= -9

n= -8 (boundary)

n= -7

-5n

 ≥ 40truetruefalse

-5n

 ≥ 40
n 

 

≥

≤

<

>

 

Answer 1

To solve the inequality \(-5n \geq 40\), let's start by isolating \(n\).

1. Divide both sides of the inequality by -5. Remember, when dividing or multiplying both sides of an inequality by a negative number, we must reverse the inequality sign.

\[
n \leq -8
\]

Now, we have the solution to the inequality.

### Solution
The solution set is:

\[
n \leq -8
\]

This means that any number less than or equal to -8 is a solution to the inequality.

### Boundary Point
- The boundary point here is indeed \(n = -8\), which means:
- The values below (like \(n = -9\)) are solutions.
- The value of \(n = -8\) is also included as a solution.
- The values above (like \(n = -7\)) are **not** solutions.

Thus, the solution can be expressed using interval notation as:

\[
(-\infty, -8]
\]

If you have any further questions or need more clarifications, feel free to ask!