Examples

    1)
    Solve the inequality |2x+3| <= 1, give the solutions as a set and graph the solution set on the number line.

      Solution:
      |2x+3| <= 1 is the same as -1.<=.2x.+.3.<.1
      Add -3 to each part to get -4.<=.2x<=.1
      Multiply each part by 1/2 to get -2.<=.x<=.-1

      Therefore the solution set is {x.:.-2.<=.x<=.-1}

      And the number line looks like: 

      _ _ _ _________________ _ _ _ _ _ _ _ _ _
       -2           -1          0
    2)
    Solve |5-4x| > 2, give the solutions as a set and graph the solution set on the number line.

      Solution:
      |5-4x| > 2 means that 5.-.4x.<.-2 or 5.-.4x.>.2
      We get -4x.<.-7 or -4x.>.-3
      This implies that x.>.-7/4 or x.<.3/4

      The solution set is {x.:.x.>.7/4}unioned with{x.:.x.<.3/4}

      The number line shows that the solution is:

      ______________o_ _ _ _ _ _o______________
             3/4         7/4
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