Question

Solve each inequality. Then graph the solution set on a number line.

$\mathbf{9}\mathit{n}\mathbf{-}\mathbf{1}\mathbf{<}\mathbf{10}\mathit{n}$

Short answer

The required solution set is represented by $\left\{n|n>-1\right\}$and the required graph is,

Step-by-step solution

Step 1. Determine the solution associated with the provided inequality.

Isolate n on any side of the provided inequality.

$\begin{array}{c}9n-1<10n\\ 9n-9n-1<10n-9n\\ -1<n\end{array}$

Step 2. Take the help of obtained inequality to write the solution set.

Make the conversion of obtained inequality to the notation named as set builder notation.

$\left\{n|n>-1\right\}$

Step 3. Represent the obtained solution set in graphical form.

The graphical representation of the obtained solution set will consist of the number greater than $-1$and there will be an open circle on $-1$because of symbol $>$.