and ![-|-9|](/tpl/images/0723/1038/a3f66.png)
Step-by-step explanation:
Given
Expression = -9
Required
Select all equivalent expressions
To do that, we examine each of the options.
First Option
![-|9|](/tpl/images/0723/1038/33b28.png)
This can be rewritten as
![-|9| = -1 * |9|](/tpl/images/0723/1038/d8701.png)
![|9| = 9](/tpl/images/0723/1038/76602.png)
So, the expression becomes
![-|9| = -1 * 9](/tpl/images/0723/1038/74dc7.png)
![-|9| = -9](/tpl/images/0723/1038/3bdcc.png)
Hence, |-9| is equivalent to -9
Second Option
![|-9|](/tpl/images/0723/1038/0cfd1.png)
![|-9| = 9](/tpl/images/0723/1038/b046b.png)
So, the expression is not equivalent to -9
Third Option
![-|-9|](/tpl/images/0723/1038/a3f66.png)
This can be rewritten as
![-|-9| = -1 * |-9|](/tpl/images/0723/1038/a6cd3.png)
![|-9| = 9](/tpl/images/0723/1038/b046b.png)
So, the expression becomes
![-|-9| = -1 * 9](/tpl/images/0723/1038/ca711.png)
![-|-9| = 9](/tpl/images/0723/1038/19bf2.png)
Hence, -|-9| is equivalent to -9
Fourth Option
![-(-9)](/tpl/images/0723/1038/3aa8c.png)
This can be rewritten as
![-(-9) = -1 *(-9)](/tpl/images/0723/1038/f844c.png)
![-(-9) = -1 *-9](/tpl/images/0723/1038/e8cbc.png)
![-(-9) = 9](/tpl/images/0723/1038/73871.png)
Hence, -(-9) is not equivalent to -9
Fifth Option
The distance from 0 to 9
This is calculated as thus;
![Difference = 9 - 0](/tpl/images/0723/1038/7402c.png)
![Difference = 9](/tpl/images/0723/1038/d2bf0.png)
Hence, the difference from 0 to 9 is not equivalent to -9