Question

|-(r+q)|=|r+q| why? If we are removing - sign then mode should also be removed...I am confused?

Answer 1

`|-(r+q)|=|-1||r+q|=|r+q|`

Explanation:

`|-(r+q)|=|-1||r+q|=|r+q|`

or

`|-(r+q)|=r+q=|r+q|`

Positive Value in Mode is remain Positive.

Answer 2

`"see explanation"`

Explanation:

`"the "color(blue)"absolute value function"` returns a positive value for whatever is inside it.

`"it is a measure of the distance a value is from the origin."`

`rArr|4|=|-4|=4`

`"since both 4 and - 4 are 4 units from the origin"`

`"and distance is always positive"`

`color(blue)"by definition"`

`|x|={((x;x>=0),(-x;x<0))`

`rArr|4|=4" and "|-4|=-(-4)=4`

`"also" |x|=sqrt(x^2)`

`rArr|-4|=sqrt((-4)^2)=4`

`rArr|r+q|=|-(r+q)|`