Chapter 3.5, Problem 32E

To determine

To write : The verbal sentence “A number divided by $\text{-3}$ is less than $\text{6}$ ” as an inequality and solve the inequality.

Answer to Problem 32E

The verbal sentence “A number divided by $\text{-3}$ is less than $\text{6}$ ”is represented as $\frac{x}{-3}<6$ . The solved inequality has the value $x>-18$ .

Explanation of Solution

Given information :

Consider the information provided in the question.

Let the number be $x$

  $\begin{array}{l}\frac{x}{-3}<6\text{ Original inequality}\\ -3.\frac{x}{-3}>6.-3\text{ Multiply each side by -3}\\ \text{ Reverse the inequality}\\ \\ x>-18\text{ Simplify}\text{.}\end{array}$

The solved inequality has the value $x>-18$ .