WholeLottaLove wrote:
(2) |x-3| <= -y
This means that x-3 is negative, so:
-(x-3)<=-y
3-x<=-y
-(3-x)<=y
This means that x-3 is negative, so:
-(x-3)<=-y
3-x<=-y
-(3-x)<=y
Dear WholeLottaLove
Your point "This means that x-3 is negative" is incorrect.
General theory is: |X| <= a, ==> -a <= X <= a
So, X does not have to be negative. X is between -a and a.
For example: |x -3| <= 9 ==> -9 <= (x -3) <=9
The KEY point is absolute value cannot be negative, thus the smallest value of |x - 3| is 0.
Because -y <= 0 ==> |x-3| must be 0 ==> x = 3.
Hope it helps.