Question

solve $-\frac{2}{3}n\leq16$. which of the following must be true about the inequality and the resulting graph? select three options.
$\square n\leq - 24$
$\square n\geq - 24$
$\square$ the circle is open.
$\square$ the circle is closed.
$\square$ the arrow points right.

Explanation:

Step1: Solve the inequality

Multiply both sides of \(-\frac{2}{3}n\leq16\) by \(-\frac{3}{2}\). Remember that when multiplying or dividing an inequality by a negative number, the inequality sign flips. So \(n\geq16\times(-\frac{3}{2})\).
\(n\geq - 24\)

Step2: Analyze the graph

Since \(n\geq - 24\), the circle at \(-24\) is closed (because the inequality is \(\geq\), including the value \(-24\)) and the arrow points to the right (towards larger numbers).

Answer:

B. \(n\geq - 24\), D. The circle is closed, E. The arrow points right