Chapter 1.6, Problem 41PPS

To determine

To write: the inequality given by the statement.

Answer to Problem 41PPS

An inequality is $\left|z+5\right|\ge 4$ .

Explanation of Solution

Given information:

Given statement

Numbers that are at least 4 units from $-5$ .

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

Numbers that are at least b units from $-a$ can be expressed as $\left|x+a\right|\ge b$ .

Calculation:

Consider the given statement,

Numbers that are at least 4 units from $-5$ .

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

So, the inequality corresponding to the verbal expression will be

  $\left|z+5\right|\ge 4$

Hence, the solution of the inequality is $\left|z+5\right|\ge 4$ .