If y is an integer and y=|x|+x

If y is an integer and y=|x|+x, is y=0?

1) x'<'0

2) y'<'1

Remember that y= x +|x|, i.e. y= 2x if x'>'0 and y = 0 otherwise

a) Suff

b) Now Y'<'1 i.e. it can be 0, -1, -2, -3. But for Y to be less than 1, x has to be negative. Because positive x will invariably give a result of 1 or higher. If x is negative, then it will never let Y to be anything else but 0. So X '<' 0.