Tuesday, February 9, 2016

What are all real solutions of the equation |2x-5|=8?

We'll apply the property of absolute value and we'll
discuss 2 cases:


2x-5 for
2x-5>=0


2x>=5


x>=5/2


-2x
+ 5 for
2x-5<0


2x<5


x<5/2


Case
1: x belongs to the interval [5/2, +infinite).


2x - 5 =
8


2x = 8+5


2x =
13


x = 13/2


Since x = 13/2
belongs to the interval [5/2, +infinite), we'll accept it as
solution.


Case 2: x belongs to the interval
(infinite,5/2).


-2x + 5 =
8


-2x = 8 - 5


-2x =
3


x = -3/2


Since x = -3/2
belongs to the interval (infinite,5/2), we'll accept it as
solution.


All real solutions of the given
equation are: {-3/2 ; 13/2}.

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