Chapter 1.5, Problem 26PPS

To determine

To write and solve: the inequality given by the statement.

Answer to Problem 26PPS

An inequality is $\frac{z+3}{6}<-2$ .

Solution is $z<-15$ .

Explanation of Solution

Given information:

Given statement

The quotient of the sum of 3 and a number and 6 is less than $-2$ .

Calculation:

Consider the given statement,

The quotient of the sum of 3 and a number and 6 is less than $-2$ .

Let us consider a variable as $z$ to write an inequality

So, the inequality will be

  $\frac{z+3}{6}<-2$

Now, solve the inequality as shown,

  $\begin{array}{c}\frac{z+3}{6}<-2\\ \frac{z+3}{6}\cdot 6<-2\cdot 6\\ z+3<-12\\ z+3-3<-12-3\\ z<-15\end{array}$

Hence, the solution of the inequality is $z<-15$ .