Sunday, May 4, 2014

Solve the absolute value inequality. |2-5x|

To solve |2-5x| < =
0


Solution:


If 2-5x is
< 0 then |2-5x| = 5x-2  by definition . So 5x-2 < 0 by
definition.


It is a
contradiction


If 2-5x > 0, then |2-5x| =2-5x by
definition. So 2-5x < 0 a contradiction.


So x
> 2/5.


2 < 5x, x
>2/5.


So x cannot be greater than 2/5 and x cannot
be less than 2/5.


Therefore x = 2/5 is the only value that
satisfies |2-5x| < = 0.


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