Rewrite without absolute value for the given conditions:

y=|x−3|+|x+2|−|x−5|, if x> 5

y=?

reply asap and explain !

Hello from MrBillDoesMath!

y = x + 4

Discussion:

As x >5,

x-3  > 5 -3 > 0

x + 2 > 5 + 2 > 0

x -5 > 5 - 5 >=0

So for the given x values each term is positive and  abs(a) = a. That is

y = (x-3) + (x+2) - (x -5)                => note abs(a) replaced by "a"

y = (x + x - x) +   ( -3 +2 + 5)        => -3 + 2 + 5 = 4

y = x + 4

Thank you,

MrB

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