SOLUTION: y = |-2x+5|-|2x-5| if x<-2.5 if x>2.5 if -2.5&#8804;x&#8804;2.5

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Question 1070069: y = |-2x+5|-|2x-5|

if x<-2.5
if x>2.5
if -2.5≤x≤2.5

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
y= |−2x+5|-|2x−5|
if x<−2.5, then 2x-5 is negative and -2x+5 is positive
So, y = -2x+5 - -(2x-5) = -2x+5+2x-5 = 0
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if x>2.5, then -2x+5 is negative and 2x-5 is positive
So y = -(-2x+5) - (2x-5) = 2x-5-2x+5 = 0
if −2.5≤x≤2.5 then y = 5-5 = 0
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Simpler solution::
Rewrite your problem as::
y = |-(2x-5)|-|(2x-5)]
Since |a| = |-a|, y = 0
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Cheers,
Stan H.
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Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
y is constantly 0 because those absolute values are equal. 
That's because what's between the first pair of absolute 
value bars is -1 times what's between the second pair.  So 
it's just equivalent to y = 0 for all values.  It is not 
necessary to take those special cases indicated.  You can 
show y = 0 for ALL values of x this way:

y = |-2x+5| - |2x-5|
y = |-1(2x-5)| - |2x-5|
y = |-1||2x-5| - |2x-5|
y = 1|2x-5| - |2x-5|
y = |2x-5| - |2x-5|
y = 0

Edwin
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