Absolute Value

Question

l x+2l < 4

Answer 1

l x+2l < 4     means

 

  A.    (x+2) < 4

          x < 2            [may subtract +2 from both sides and retain sense of inequality]

 

 

AND:      [note: ">" or "=" mean "OR" ]

  B.    -(x+2) < 4

          -x -2 < 4

             -x < 6        [may add +2 to both sides and retain sense of inequality]

             x > -6      [multiply by (-1) reverses sense of inequality]

 

So,  -6 < x < 2      [This is pattern for "&lt"]

 

Test case 1.  x=-7

              |-7+2| <  4   ?

                 |-5| < 4    ?

                    5 < 4   ? No, as expected

 

Test case 2:   x=0

              |0+2| < 4   ?

                  2 < 4   ?Yes, as expected

 

Test case 3:   x=10

             |10+2| < 4   ?

                 12 < 4   ?No, as expected