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Order the following pair of numbers using [tex]\ \textless \ , \ \textgreater \ [/tex], or [tex]=[/tex]:

[tex]|-5| \quad \text{and} \quad -|-5|[/tex]

Select the correct answer below:

A. [tex]\ \textless \ [/tex]

B. [tex]\ \textgreater \ [/tex]

C. [tex]=[/tex]

Sagot :

GinnyAnsweridn
To solve the problem, we need to compare the values of two expressions: [tex]\(|-5|\)[/tex] and [tex]\(-|-5|\)[/tex]. Let’s break this down step-by-step.

1. Evaluate [tex]\(|-5|\)[/tex]:
- The absolute value of a number is its distance from zero on the number line, without considering direction.
- For [tex]\(-5\)[/tex], the absolute value is calculated as follows:
[tex]\[ |-5| = 5 \][/tex]

2. Evaluate [tex]\(-|-5|\)[/tex]:
- First, find the absolute value of [tex]\(-5\)[/tex], which we already determined to be [tex]\(5\)[/tex].
- Then, take the negative of this absolute value:
[tex]\[ -|-5| = -5 \][/tex]

3. Compare the two values:
- We now have [tex]\(|-5| = 5\)[/tex] and [tex]\(-|-5| = -5\)[/tex].
- Clearly, [tex]\(5\)[/tex] is greater than [tex]\(-5\)[/tex].

Therefore, the correct inequality is:
[tex]\[ 5 > -5 \][/tex]

Hence, the correct symbol to order the numbers is:

\[>|
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