Chapter 1, Problem 42SGR

To determine

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

Answer to Problem 42SGR

The solution is given by $p>-2$ .

Explanation of Solution

Given information:

Given inequality

  $-p-13<3\left(5+4p\right)-2$

Calculation:

Consider the given inequality,

  $-p-13<3\left(5+4p\right)-2$

Now, solve the inequality as shown,

  $\begin{array}{c}-p-13<3\left(5+4p\right)-2\\ -p-13<15+12p-2\\ -p-13-12p<15+12p-2-12p\\ -13p-13<13\\ -13p-13+13<13+13\\ -13p<26\\ \frac{-13p}{-13}>\frac{26}{-13}\\ p>-2\end{array}$

Now, graph the inequality as shown:

  

The open ball suggests that the solution region is not included the point $-2$ .

Greater than sign indicates the region is right side to the point $-2$ on number line.

Hence, the solution of the inequality is $p>-2$ .