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 

 

≥

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>

≤

 

Answer 1

To solve the inequality \(-5n \geq 40\), we can follow these steps:

1. **Divide both sides by -5**: When dividing or multiplying by a negative number in an inequality, we must flip the inequality sign.

\[
n \leq \frac{40}{-5}
\]

\[
n \leq -8
\]

This tells us that \(n\) can take any value less than or equal to \(-8\). Thus, the boundary point is \(n = -8\), which we established as the point separating the solution from non-solution values.

2. **Determine the solution set**:
- Values less than or equal to \(-8\) are solutions.
- So the complete solution to the inequality \(-5n \geq 40\) is:

\[
n \leq -8
\]

Now, based on the values provided:
- \(n = -9\) is included in the solution since it is less than \(-8\).
- \(n = -8\) is also included in the solution since it is the boundary point.
- \(n = -7\) is not included in the solution since it is greater than \(-8\).

In conclusion, the solution to the inequality \(-5n \geq 40\) is:

\[
n \leq -8
\]