Chapter 1.3, Problem 41E

To determine

Represent thenumbers from increasingorder.

  $9,\left|-4\right|,-4,5,\left|2\right|$

Answer to Problem 41E

The number from least to greatest is given as:

  $-4,\left|2\right|,\left|-4\right|,5,9$

Explanation of Solution

Given:

The numbers:

  $9,\left|-4\right|,-4,5,\left|2\right|$

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:

  $\begin{array}{l}|-a|=a,a>0\Rightarrow \left|-4\right|=4\\ \left|a\right|=a,a\ge 0\Rightarrow \left|2\right|=2\end{array}$

Now, the given value can be written as:

  $9,4,-4,5,2$

The least number among all these numbers are -4, then 2 is the second least, and in the same way the numbers are 4, 5 and 9.

Thus, the number from least to greatest is given as $-4,2,4,5,9$ .

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

  $-4,\left|2\right|,\left|-4\right|,5,9$