Chapter 1.9, Problem 23WE

To determine

To use: The suitable symbols $>,<,\text{or }=$ in the given statement.

Answer to Problem 23WE

  $\left|-8\right|\underset{\_}{\text{}\text{ < }}\left|-10\right|$

Explanation of Solution

Given information:

The given statement is $\left|-8\right|\underset{\_}{\text{ ? }}\left|-10\right|$

Concept Used:

• To evaluate an expression having one or more than one variable at the given value of the variable(s), put the given values of variable(s) in their respective place, and evaluate the value of expression.
• $\left|a\right|=a;\text{ if }a\ge 0$
• $\left|a\right|=-a;\text{ if }a<0$
• $a+\left(-b\right)=a-b$
• $a-\left(-b\right)=a+b$
• $a-\left(+b\right)=a-b$

Calculation:

To evaluate the expression

  $\left|-8\right|\underset{\_}{\text{}}\left|-10\right|$

Calculate the value $\left|-8\right|$ :

  $\begin{array}{l}\left|a\right|=-a;\text{ if }a<0;\text{ if }a<0\\ \text{Here }-8<0\\ \left|-8\right|=-\left(-8\right)=8\end{array}$

Now, calculate the value $\left|-10\right|$ :

  $\begin{array}{l}\left|a\right|=-a;\text{ if }a<0;\text{ if }a<0\\ \text{Here }-10<0\\ \left|-10\right|=-\left(-10\right)=10\end{array}$

Now, the value of 10 is greater than 8. So, replace the above obtained value in the given statement:

  $\begin{array}{c}\left|-8\right|\underset{\_}{\text{}}\left|-10\right|\\ 8\underset{\_}{\text{}\text{ < }}10\end{array}$

Thus,

  $\left|-8\right|\underset{\_}{\text{}\text{ < }}\left|-10\right|$