Chapter 1.6, Problem 33PPS

To determine

To solve: the given inequality and graph the solution on number line.

Answer to Problem 33PPS

The solution is given by $2<k<4$ .

Explanation of Solution

Given information:

Given inequality

  $16<6k+4<28$

Calculation:

Consider the given inequality,

  $16<6k+4<28$

Now, solve the inequality as shown,

  $\begin{array}{c}16<6k+4<28\\ 16-4<6k+4-4<28-4\\ 12<6k<24\\ \frac{12}{6}<\frac{6k}{6}<\frac{24}{6}\\ 2<k<4\end{array}$

Hence, the solution of the inequality is $2<k<4$ .

Now, graph the inequality as shown:

  

The open ball suggests that the solution region is not included the points $2$ and $4$ .

The sign indicates the region is left side to the point $4$ and right side to the point $2$ on number line.