Absolute Value Inequalities - PowerPoint by Udc4XK1S

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									 Absolute
   Value
Inequalities




               Algebra
          Solving an Absolute-Value Inequalities



                        x 6

8 7 6 5 4 3 2 1   0       1       2       3       4       5       6   7   8


                          x 6

8 7 6 5 4 3 2 1       0       1       2       3       4       5   6   7   8
    Graphing Absolute Value
• When an absolute value is greater than
  the variable you have a disjunction to
  graph.      x 4
• When an absolute value is less than
  the variable you have a conjunction to
  graph.      x 4
           Solving an Absolute-Value Inequality


            Solve | x  4 | < 3


           x  4 IS POSITIVE           x  4 IS NEGATIVE
             |x4|3                     |x4|3
               x  4  3                  x  4  3
                   x7                            x1
                                                        Reverse
                                                        inequality symbol.

The solution is all real numbers greater than 1 and less than 7.

    This can be written as 1  x  7.
Solving an Absolute-Value Inequality

2x + 1  POSITIVE 2x the solution.
Solve | 2x IS1 | 3  6 and graph + 1 IS NEGATIVE
 | 2x  1 |  3  6        | 2x  1 | 3  6
2x + 1 IS POSITIVE        2x + 1 IS NEGATIVE
 | 2x|2x| 31 |6 9
        1                | 2x|2x|  1 |6  9
                                  1 3 
    | 2x   |1  +9
       2x 1  9                  2x |1  9
                               | 2x 1  9
          2x  8
      2x  1  +9
                                     2x 10
                                 2x  1 9
           x4                         x  5
            2x  8                      2x  10
The solution is all real numbers greater than or equal
             x4                         x  5
to 4 or less than or equal Reverse can be written as
                           to  5. This
the compound inequality inequalityx  4.
                           x   5 or
                           symbol.

 6 5 4 3 2 1         0   1   2   3   4   5   6
              Strange Results

   2(3x  8)  7  5          True for All Real Numbers,
                               since absolute value is
                               always positive, and
                               therefore greater than any
                               negative.

(2[3x  (8  4)]  12)3  2      No Solution Ø.
                                  Positive numbers are
                                  never less than
                                  negative numbers.
 Absolute
   Value
Inequalities




               Algebra

								
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