Chapter 1.3, Problem 44E

To determine

Represent thenumbers from increasingorder.

  $-\left|-3\right|,\left|0\right|,-1,\left|2\right|,-2$

Answer to Problem 44E

The number from least to greatest is given as:

  $-\left|-3\right|<-2<-1<\left|0\right|<\left|2\right|$

Explanation of Solution

Given:

The numbers:

  $-\left|-3\right|,\left|0\right|,-1,\left|2\right|,-2$

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:

  $\begin{array}{c}-\left|-3\right|=-3\left\{\left|a\right|=a,a\ge 0\right\}\\ \left|0\right|=0\left\{\left|a\right|=a,a\ge 0\right\}\\ \left|2\right|=2\left\{\left|a\right|=a,a\ge 0\right\}\end{array}$

Now, the given value can be written as:

  $-3,0,-1,2,-2$

The least number among all these numbers are - 3, then - 2 is the second least, and in the same way the numbers are -1, 0and 2.

Thus, the number from least to greatest is given as $-3<-2<-1<0<2$ .

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

  $-\left|-3\right|<-2<-1<\left|0\right|<\left|2\right|$