Answer:
[tex]-|9|[/tex] and [tex]-|-9|[/tex]
Step-by-step explanation:
Given
Expression = -9
Required
Select all equivalent expressions
To do that, we examine each of the options.
First Option
[tex]-|9|[/tex]
This can be rewritten as
[tex]-|9| = -1 * |9|[/tex]
[tex]|9| = 9[/tex]
So, the expression becomes
[tex]-|9| = -1 * 9[/tex]
[tex]-|9| = -9[/tex]
Hence, |-9| is equivalent to -9
Second Option
[tex]|-9|[/tex]
[tex]|-9| = 9[/tex]
So, the expression is not equivalent to -9
Third Option
[tex]-|-9|[/tex]
This can be rewritten as
[tex]-|-9| = -1 * |-9|[/tex]
[tex]|-9| = 9[/tex]
So, the expression becomes
[tex]-|-9| = -1 * 9[/tex]
[tex]-|-9| = 9[/tex]
Hence, -|-9| is equivalent to -9
Fourth Option
[tex]-(-9)[/tex]
This can be rewritten as
[tex]-(-9) = -1 *(-9)[/tex]
[tex]-(-9) = -1 *-9[/tex]
[tex]-(-9) = 9[/tex]
Hence, -(-9) is not equivalent to -9
Fifth Option
The distance from 0 to 9
This is calculated as thus;
[tex]Difference = 9 - 0[/tex]
[tex]Difference = 9[/tex]
Hence, the difference from 0 to 9 is not equivalent to -9
