Chapter 3.3, Problem 14PPE

To determine

To solve: the given inequality and graph the solution. Check the result.

Answer to Problem 14PPE

The solution is $k<12$ .

Explanation of Solution

Given information:

Given inequality

  $8>\frac{2}{3}k$

Calculation:

First solve the inequality $8>\frac{2}{3}k$ . Then

  $\begin{array}{c}8>\frac{2}{3}k\\ \frac{3}{2}\left(8\right)>\frac{3}{2}\left(\frac{2}{3}\right)k\\ \frac{24}{2}>k\\ k<12\end{array}$

It is to be draw the graph of $k<12$ . Now $k<12$ means all real numbers $k$ that are less than 12. Since 12 is not a solution, draw an open dot at 12. The numbers less than 12 are to the left of 12 on the number line. Shade to the left of 12. Therefore, the graph is

  

To check the inequality symbol of $k<12$ , ,make sure that a number greater than 12 is a solution of the original inequality. To check this substitute $k=0$ into the original inequality. Therefore,

  $\begin{array}{l}8>\frac{2}{3}\times 0\\ 8>0\end{array}$

Hence, the solution is $k<12$ .