Question

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

	n = -9	n = -8 (boundary)	n = -7
-5n ≥ 40	true	true	false

-5n ≥ 40
n

Explanation:

Step1: Analyze the inequality and test points

We have the inequality \(-5n \geq 40\). Let's analyze the test points:

• For \(n = -9\), \(-5\times(-9)=45\), and \(45\geq40\) (true).
• For \(n = -8\), \(-5\times(-8) = 40\), and \(40\geq40\) (true).
• For \(n=-7\), \(-5\times(-7)=35\), and \(35\geq40\) (false).

Step2: Solve the inequality algebraically

Start with \(-5n \geq 40\). Divide both sides by \(-5\). Remember that when dividing or multiplying an inequality by a negative number, the direction of the inequality sign flips. So we get \(n \leq -8\).

Answer:

\(n \leq -8\) (with the inequality symbol \(\leq\) and the number \(-8\))