Chapter 1.3, Problem 43E

To determine

Represent thenumbers from increasingorder.

  $-18,\left|-24\right|,-19,\left|-18\right|,\left|22\right|$

Answer to Problem 43E

The number from least to greatest is given as:

  $-19<-18<\left|-18\right|<\left|22\right|<\left|-24\right|$

Explanation of Solution

Given:

The numbers:

  $-18,\left|-24\right|,-19,\left|-18\right|,\left|22\right|$

Concept Used:

• To use the absolute function which is defined as :

  $f\left(x\right)=\{\begin{array}{cc}x& \text{ if }x\ge 0\\ -x& \text{if }x<0\end{array}$

Or Apply the absolute rule:

  $\begin{array}{l}|-a|=a,\text{}a>0\\ \left|a\right|=a,a\ge 0\end{array}$

Calculation:

First there are two number which are in the modulus form, simply those numbers:

  $\begin{array}{c}-18,\left|-24\right|,-19,\left|-18\right|,\left|22\right|\\ \left|-24\right|=24\left\{|-a|=a,a>0\right\}\\ \left|22\right|=22\left\{\left|a\right|=a,a\ge 0\right\}\\ \left|-18\right|=18\left\{|-a|=a,a>0\right\}\end{array}$

Now, the given value can be written as:

  $-18,24,-19,18,22$

The least number among all these numbers are - 19, then - 18 is the second least, and in the same way the numbers are 18, 22 and 24.

Thus, the number from least to greatest is given as $-19<-18<18<22<24$ .

Hence, the given number from least to greatest is given as:

  $-19<-18<\left|-18\right|<\left|22\right|<\left|-24\right|$