Question

graph the solution to the inequality $-\frac{1}{3}n > 32$.

Explanation:

Step1: Solve the inequality

Multiply both sides of the inequality \(-\frac{1}{3}n>32\) by \(- 3\). Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign changes. So we have \(n<32\times(-3)\), which simplifies to \(n < - 96\).

Step2: Analyze the graph

The solution \(n < - 96\) means that on the number - line, there is an open circle at \(-96\) (because \(n=-96\) is not included in the solution set) and the line extends to the left (towards more negative numbers).

Answer:

The fourth graph (the one with an open circle at \(-96\) and the line extending to the left on the number - line with negative values) is the correct graph of the solution \(n < - 96\).