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Solving Absolute Value Inequalities
Absolute Value inequalities may be solved using the general methods for solving
inequalities – see
http://www.mathmotivation.com/lectures/Inequalities.pdf
. In summary
you replace the inequality symbol with =, solve this equation to find the critical numbers,
plot the critical numbers, and test the intervals. For example, the inequality
x  2
< 3
may be solved by first solving
x  2
= 3 to get x=5 and x=1. (See
http://www.mathmotivation.com/lectures/AbsoluteValueEquations.pdf
). Then, plot the
critical numbers x = 5 and x = 1 on the number line and check the intervals.
The test value of Interval Two, x=0 results in a true statement when substituted into
x 2
< 3
where as the test values of Interval One and Interval Three, x = 2 and x =6,
result in false statements. So Interval Two, makes up the solution, i.e. –1< x < 5.
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 Fall '09
 Crandall
 Anthropology, Negative and nonnegative numbers

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