Question

solve the inequality and graph the solution.

-1 < \frac{n}{6}

plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Multiply both sides by 6

Multiply each side of the inequality \(-1<\frac{n}{6}\) by \(6\) to isolate \(n\). Using the property of inequalities (if \(a < b\) and \(c>0\), then \(ac < bc\)), we get \(-1\times6<\frac{n}{6}\times6\).
$$- 6 < n$$

Step2: Graph the solution

The inequality \(n>-6\) means that \(n\) can take any value greater than \(-6\). On the number - line, we place an open circle at \(-6\) (because \(-6\) is not included in the solution set, since the inequality is \(n > - 6\) not \(n\geq - 6\)) and draw a ray to the right of \(-6\).

Answer:

The solution of the inequality is \(n > - 6\). On the number - line, there is an open circle at \(-6\) and a ray extending to the right.