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=>Condition 1) |x+5|=|y+5| is equivalent to \((x+5)^2=(y+5)^2 or (x+5)^2-(y+5)^2 = 0.\) \((x+5)^2-(y+5)^2 = (x+y+10)(x-y) = 0.\) Then \(x = y or x + y + 10 = 0.\) Since x cannot be equal to \(y, x + y = -10.\) This is sufficient.

Condition 2) |x+5|=|y+5| is equivalent to \((x+5)^2=(y+5)^2 or (x+5)^2-(y+5)^2 = 0.\) \((x+5)^2-(y+5)^2 = (x+y+10)(x-y) = 0.\) Then x = y or x + y + 10 = 0. Since x > 3 and y < 3, x is not equal to y. Thus x + y = -10. This is sufficient.

you have written |x+5|=|y+5| implies (x+5)= (y+5) or (x+5) = -(y+5) which should mean x+y = - 10 , you have written x+y =0?? Can you enlighten me x+y = 0?? in case when x not equal to y

it should be x+y = -10

AND i can see in your solution everywhere is x+y = 0 ?? guess you have mistakenly forgot -10..

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If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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31 Aug 2017, 02:03

pclawong wrote:

Can anyone explain the statement 2?

For the statement 1, I got x>0; y<0 then x+5=-y-5 x+y=-10

2) x>3 and y <3 i guess you must be confused what if y=2 then x will be x+2=-10 , x= -12 but do tell me : is the solution x= -12 > or < 3, if it does not satisfy you condition 2 then it is not your solution and you can not take this value. on other hand Let x=4 y = -10-4 , y =-14 means this value is satisfying your condition 2 hence they are correct values. you cant take 0,0 either as x is > 3 so we cant take those values as well Therefore sufficient
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