Chapter EP, Problem 1.5.11EP

To determine

To solve: The inequality $8\left(2c-1\right)>11c+22$ and then plot the graph of the solution set on a number line.

Answer to Problem 1.5.11EP

The solution of the inequality $8\left(2c-1\right)>11c+22$ is $c>6$ , and graph of the solution set of the inequality is shown in figure (1).

Explanation of Solution

Given:

The inequality is $8\left(2c-1\right)>11c+22$ .

Calculation:

Expand the inequality $8\left(2c-1\right)>11c+22$ as follows.

  $\begin{array}{c}8\left(2c-1\right)>11c+22\\ 16c-8>11c+22\\ 16c-11c>22+8\\ 5c>30\end{array}$

Divide both sides of the inequality $5c>30$ by $5$ .

  $\begin{array}{c}\frac{5c}{5}>\frac{30}{5}\\ c>6\end{array}$

Therefore, the solution of the inequality $8\left(2c-1\right)>11c+22$ is $c>6$ .

The graph of the solution set of the inequality is as follows.

Figure (1)

The graph for the inequality $c>6$ contains all values that are greater than 6 and dot shows 6 is included in solution set.

Therefore, the solution of the inequality $8\left(2c-1\right)>11c+22$ is $c>6$ , and graph of the solution set of the inequality is shown in figure (1).