Chapter 1.5, Problem 46HP

To determine

To find: whether the following statement is sometimes, always, or never true.

Answer to Problem 46HP

The statement is sometime true

Explanation of Solution

Given information:

Given statements

“The opposite of the absolute value of a negative number is less than the opposite of that number”.

Calculation:

Let, consider the number $x$ .

Absolute value of $-x$ is equal $x$ , but need opposite of that, so first part of sentence gives us our final $-x$ .

Second part of sentence says that need opposite number of the number, get in first sentence.

So, $-x$ opposite is $x$ .

Now, let’s see,

  $-x<x$

So, the statement is sometime true. For example if $x=1$ then $-1<1$ which is true, but if $x=-1$ then $1<-1$ which is not true statement.