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
-----------------------------------------------
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
----
Simpler solution::
Rewrite your problem as::
y = |-(2x-5)|-|(2x-5)]
Since |a| = |-a|, y = 0
-------------
Cheers,
Stan H.
---------------
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
(