Question

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

1. $-9c<126$
   
2. $-25<\frac{p}{-5}$
   

Short answer

(a) The solution interval for inequality (a) is $\left(-14,\infty \right)$and representation on number line is :-

(b) The solution interval for inequality (b) is $\left(-\infty ,125\right)$and representation on number line is :-

Step-by-step solution

Step 1. Part (a) Given and Solution

We have given the following inequality :-

$-9c<126$.

To solve the inequality divide both sides by -9, then we have :-

$$\begin{gathered} \frac{-9c}{-9}>\frac{126}{-9} \\ c>-14 \end{gathered}$$

So the solution interval is $\left(-14,\infty \right)$.

Representation of solution on number line is as following :-

Step 2. Part (b) Given and solution

Here we have given the following inequality :-

$-25<\frac{p}{-5}$.

To solve the inequality multiply both sides -5, then we have :-

$$\begin{gathered} -25\times -5>\frac{p}{-5}\times -5 \\ \Rightarrow -125>p \\ orp<-125 \end{gathered}$$

So the solution interval is $\left(-\infty ,-125\right)$.

Representation of solution on number line is as following :-