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Compound and Absolute Value Inequalities

VIEWS: 9 PAGES: 11

									1.6 Compound and Absolute
     Value Inequalities
    Compound inequalities are just
    more than one inequality at the
             same time.



Sometimes, they are connected by AND.
Sometimes, they are connected by OR.
Solving an “AND” inequality
  AND means “these two items must
  both be true”. It is the intersection
         of two inequalities.


  Our strategy will be to solve the two
inequalities separately and then put the
           solutions together.
   Solving an “AND” inequality
          Solve: 11 < 2x + 5 < 19

     First, let’s find the two inequalities.

To find them, we just include:
1) The middle expression
2) An inequality symbol
3) Everything across the symbol from the
   middle.
Solving an “AND” inequality
       Solve: 11 < 2x + 5 < 19

11 < 2x + 5                        2x + 5 < 19
 6 < 2x                                 2x < 14
 3<x                                     x<7
          Now it’s time to put our
          inequalities back together!

                3<x<7
  Graphing an “AND” inequality
          Solve: 11 < 2x + 5 < 19
        Solution:       3<x<7

                    3   4   5   6   7

 3<x

 x<7

3<x<7
 Solving an “OR” inequality
  OR means “at least one of the two
  items must both be true”. It is the
      union of two inequalities.


  Our strategy will be to solve the two
inequalities separately and then put the
           solutions together.
   Solving an “OR” inequality
      Solve: x - 2 > -3 or x + 4 < -3



Finding the two inequalities is a bit easier;
      they are already listed separately.
Solving an “OR” inequality
Solve: x - 2 > -3 or x + 4 < -3

x - 2 > -3                        x + 4 < -3
   x > -1                             x < -7

        Now it’s time to put our
        inequalities back together!

             x > -1 or x < -7
      Graphing an “OR” inequality
       Solve:      x - 2 > -3 or x + 4 < -3
            Solution: x > -1 or x < -7

                  -7   -6   -5   -4   -3   -2   -1
  x > -1

 x < -7

x > -1 or
x < -7
  Graphing an Absolute Inequality
            Graph:         |x| < 4
    This means the distance from zero is < 4
              -6 -4   -2     0   2   4   6
|x| < 4

            Graph:         |x| > 4
    This means the distance from zero is > 4
              -6 -4   -2     0   2   4   6
|x| > 4
Solving Absolute Value Inequalities.

      When we need to use two cases
         to solve an absolute value
      problem, treat the problem like an
         OR inequality for graphing.

								
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