Chapter EP, Problem 1.5.2EP

To determine

To solve: The inequality $3r-8>7$ and then plot the graph of the solution set on a number line.

Answer to Problem 1.5.2EP

The solution of the inequality $3r-8>7$ is $r>5$ , and graph of the solution set of the inequality is shown in figure (1).

Explanation of Solution

Given:

The inequality is $3r-8>7$ .

Calculation:

Subtract 7 from both sides of the inequality $3r-8>7$ .

  $\begin{array}{c}3r-8-7>7-7\\ 3r-15>0\end{array}$

Add $15$ to both sides of the inequality $3r-15>0$ .

  $\begin{array}{c}3r-15+15>0+15\\ 3r>15\\ r>\frac{15}{3}\\ r>5\end{array}$

Therefore, the solution of the inequality $3r-8>7$ is $r>5$ .

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

Figure (1)

The graph for the inequality $r>5$ contains all values that are greater than 5 and dot shows 5 is not included in solution set.

Therefore, the solution of the inequality $3r-8>7$ is $r>5$ , and graph of the solution set of the inequality is shown in figure (1).