# Lesson 6.4 Absolute Value Inequalities

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```					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

|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

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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 views: 7 posted: 4/7/2012 language: English pages: 9