SOLUTION: How do I write y = |2x-4| in a piecewise expression.

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Question 477012: How do I write y = |2x-4| in a piecewise expression.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
y = |2x-4|
when 2x-4 is positive or zero then y = 2x-4
when 2x-4 is negative then y = -(2x-4)

That is,

when 2x-4 ≧ 0 then y = 2x-4
when 2x-4 < 0 then y = -(2x-4)

Solve 2x-4 ≧ 0
        2x ≧ 4
         x ≧ 2

Solve 2x-4 < 0
        2x < 4
         x < 2

Therefore 

when x ≧ 2, then y = 2x-4
when x < 2, then y = -(2x-4)

Normally that is written:

 

And you might want to write -(2x-4) as -2x+4

 

Sometimes they put "if" instead of "when"



And sometimes they just put a comma there,



Edwin