Chapter 1.7, Problem 14E

To determine

To calculate: The solution of the given inequality, $10x<-40$, and graph the solution set.

The solution set of the given inequality, $10x<-40$, is $x<-4$.

Calculation:

Consider the given inequality, $10x<-40$.

Multiply each part by $\frac{1}{10}$ by using the multiplicative property of an inequality, according to which, if $c>0$, then $a<b$ becomes $ac<bc$ and if $c<0$, then $a>b$ becomes $ac<bc$.

$\begin{array}{c}10x<-40\\ x<-4\end{array}$

Hence, the solution set of the given inequality is the set of all real numbers that are smaller than $-4$ which can be denoted by $\left(-\infty ,-4\right)$.

Graph:

The solution set of the inequality is shown in the graph.

The parenthesis at $x=-4$ means that the value at $x=-4$ is not included in the solution set of the inequality.