Question

Simplify. Consider all cases: |(x−19)+11|

___ if x > ___

___ if x = ___

___ if x < ___

Answer 1

x-8 if x>0

-8 if x=0

-x-8 if x<0

Explanation:

Given that that,

|(x-19)+11|

Case I:

If the value of x greater than 0. It means the value of x is positive.

So we plug x= +x in the above expression.

(+x-19)+11

=x-19+11

=x-8

x-8 if x>0

Case II:

If the vale of x is equal to zero.

We plug x= 0 in the above expression.

(0-19)+11

= -19+11

= - 8

-8 if x=0

Case III

If the value of x lesser than 0. It means the value of x is always negative.

So we plug x= -x in the above expression.

(-x-19)+11

= - x-19+11

= - x-8

-x-8 if x<0