Lesson 6.4 Absolute Value Inequalities

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Lesson 6.4 Absolute Value Inequalities Powered By Docstoc
					6.4: Absolute
 Values and
 Inequalities
Conjunction: |ax + b| < c

Means: x is between + c

      -c < ax +b < c
Disjunction:     |ax +b| > c

Means:     not between!

ax + b < -c or     ax + b > c
Solving absolute inequalities
       and graphing:
|x - 4| < 3      (less than is betweeness)

Means:    -3 < x- 4 < 3 (solve)
          +4      +4 +4

              1< x< 7
Graph:

         0 1 2 3 4 5 6 7 8 9
Solve and graph:

|x + 9 |> 13    (disjunction)

Means: x + 9 < -13     or      x + 9 > 13
          -9     -9                  -9   -9
           x < -22                   x>4
Graph:

         -25 -20 -15 -10 -5 0 5 10
Change the graph to an absolute value
  inequality:
            0 1 2 3 4 5 6 7 8 9 10

1. Write the inequality. (x is between)

               2<x<8

2. Find half way between 2 and 8
   It’s 5 (this is the median)
   To find the median, add the two numbers
   and then divide by 2.        2+8 = 5
                                 2
3. Now rewrite the inequality and
subtract 5 (the median) from each section.
     2-5<x-5<8-5

Combine like terms or numbers and you
get -3 < x - 5 < 3

4. Write your absolute inequality
    |x - 5| < 3

Notice: The median is 3 units away
from either number.
Write the inequality for this disjunction:

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

 1. x < -6        or    x>4     (find the median)
   +1 +1               +1 +1       (subtract -1 from both
                                   sides, so add 1)


 2. x + 1 < - 5               x+1 > 5

                   (write x + 1 inside the absolute
 3. |x+1|>5        brackets and 5 outside positive)
Quick rule:
|x - median| ( inequality symbol here) range 2

  Median:
  add the two numbers together and divide
  by 2. Remember to subtract. Watch signs!
  Range:
  subtract the two numbers, then divide by 2.

				
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posted:4/7/2012
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