To remove the absolute value bars of
|Ax + B| < C , where C is a positive number, write this:
-C < Ax + B < C
Then solve that for x in the middle. The solution set will
usually be of the form:
(D, E)
Your example 4:
|2x + 1| < 5
-5 < 2x + 1 < 5
Add -1 to all three sides:
-6 < 2x < 4
Divide through by 2 (That will NOT reverse the < signs)
-3 < x < 2
Graph:
---------o===================o--------
-5 -4 -3 -2 -1 0 1 2 3 4
Interval notation:
(-3, 2)
[x] +6 < 10
Your example 6:
|x| + 6 < 10
Isolate the |x| by subtracting 6 from both sides:
|x| < 4
-4 < x < 4
Graph:
-----o===============================o--------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
Interval notation:
(-4, 4)
---------------------------------------
To remove the absolute value bars of
|Ax + B| > C , where C is a positive number, write this:
Ax + B < -C OR Ax + B > C
Then solve that for x in each part, leaving the word "OR" between them
The solution usually will be of this form:
(
, D) U (E, 
)
Your example 2:
|x - 5| > 2
x - 5 < -2 OR x - 5 > 2
Add 5 to borth sides of both parts:
x < 3 OR x > 7
Graph:
<====================o---------------o===========>
-2 -1 0 1 2 3 4 5 6 7 8 9 10
Solution set:
(, 3) U (7,)
Edwin
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