How do you know if an absolute value question is an " and " or an " or " problem?

Question

Will you always  have two solutions to an absolute value problem?

Answer 1

And is necessary , and or is sufficient condition.

 

     Like if:

        

          l X l   < 7  

 

     - 7 < X < 7                   -7---------+7                   

 

    

 Solution of X in addition to be less than +7 has to be greater than -7 at the same time.(and)

    However:

 

      l X l > 7

 

        X > 7 or X < -7             --------- -7           +7 -----------  

 

        Here either X =-8   or  X = +8 are sufficient to be the solution.