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Answer to Question #21967 in Algebra for jir

Question #21967
/x-5/=/x/ find (x)
Expert's answer
Consider three cases of x.
1) x in (-infinity, 0)
Then x-5<0 and x<0, whence
|x-5| =-(x-5)=-x+5
|x| = -x
and so we get the following equation
-x+5=-x
5=0
which is impossible. 2) x in [0,5]
Then x-5<=0 and x>=0, whence
|x-5| = -x+5
|x| = x
and so we get the following equation
-x+5=x
5=2x
x=2.5
3) x in (5, +infinity)
Then x-5>0 and x>0, whence
|x-5| = x-5
|x| = x
and so we get the following equation
x-5=x
-5=0
which is again impossible.
So we obtain a unique solution: x=2.5

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