Chapter 1.6, Problem 42PPS

To determine

To write: the inequality given by the statement.

Answer to Problem 42PPS

An inequality is $\left|z-1\right|\le \frac{3}{8}$ .

Explanation of Solution

Given information:

Given statement

Numbers that are no more than $\frac{3}{8}$ units from $1$ .

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 no more than b units from $a$ can be expressed as $\left|x-a\right|\le b$ .

Calculation:

Consider the given statement,

Numbers that are no more than $\frac{3}{8}$ units from $1$ .

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

So, the inequality corresponding to the verbal expression will be

  $\left|z-1\right|\le \frac{3}{8}$

Hence, the solution of the inequality is $\left|z-1\right|\le \frac{3}{8}$ .